{"id":67,"date":"2023-09-17T07:20:31","date_gmt":"2023-09-17T07:20:31","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/"},"modified":"2023-09-17T07:20:31","modified_gmt":"2023-09-17T07:20:31","slug":"%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/","title":{"rendered":"\u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0634\u0631\u062d\u0627 \u0644\u0645\u0627\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646 \u0648\u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u062a\u0647\u0627. \u064a\u0645\u0643\u0646\u0643 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646 \u062a\u0631\u0649 \u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637 \u0630\u0644\u0643 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644). \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0628\u0634\u0623\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0648\u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635\u0647\u0627. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u0646\u0634\u0631\u062d \u0627\u0644\u0641\u0636\u0648\u0644 \u0648\u0631\u0627\u0621 \u0623\u0635\u0644 \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u062c\u062f\u064b\u0627. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-binomio-de-Newton\"><\/span> \u0645\u0627 \u0647\u064a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u061f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee;text-align:right;direction:rtl\"> \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c <strong>\u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646<\/strong> \u060c \u0648\u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0633\u0645 <strong>\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<\/strong> \u060c \u0647\u064a \u0635\u064a\u063a\u0629 \u062a\u0633\u0645\u062d \u0644\u0643 \u0628\u062d\u0633\u0627\u0628 \u0642\u0648\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0633\u0647\u0648\u0644\u0629. \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631\u060c \u062a\u062a\u0643\u0648\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0645\u0646 \u0635\u064a\u063a\u0629 \u064a\u0645\u0643\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644\u0647\u0627 <sup>\u062d\u0644<\/sup> \u0627\u0644\u062a\u0639\u0627\u0628\u064a\u0631 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0635\u0648\u0631\u0629 (\u0623+\u0628).<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0627\u0644\u0648\u0627\u0636\u062d \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0633\u0645\u064a\u062a \u0639\u0644\u0649 \u0627\u0633\u0645 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0648\u0627\u0644\u0641\u064a\u0644\u0633\u0648\u0641 \u0627\u0644\u0633\u064a\u0631 \u0625\u0633\u062d\u0627\u0642 \u0646\u064a\u0648\u062a\u0646. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0647\u0646\u0627\u0643 \u0628\u0639\u0636 \u0627\u0644\u062c\u062f\u0644 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0635\u062f\u062f \u062d\u064a\u062b \u062a\u0645 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0646\u0635\u0648\u0635 \u0634\u0631\u0642 \u0623\u0648\u0633\u0637\u064a\u0629 \u062d\u064a\u062b \u0643\u0627\u0646\u062a \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0642\u064a\u062f \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0628\u0627\u0644\u0641\u0639\u0644. \u0623\u062f\u0646\u0627\u0647 \u0633\u0646\u0646\u0627\u0642\u0634 \u0628\u0639\u0645\u0642 \u0623\u0635\u0644 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Formula-del-binomio-de-Newton\"><\/span>\u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0643\u0645\u0627 \u0631\u0623\u064a\u0646\u0627 \u0641\u064a \u062a\u0639\u0631\u064a\u0641 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u0641\u0625\u0646 \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u062a\u0633\u062a\u062e\u062f\u0645 \u0644\u062d\u0644 \u0642\u0648\u0649 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646. \u0644\u0643\u0646&#8230; \u0643\u064a\u0641 \u064a\u062a\u0645 \u062a\u0637\u0628\u064a\u0642 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u061f \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631 \u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646\u061f <\/p>\n<div style=\"background-color:#ffebee;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border-radius:20px;;text-align:right;direction:rtl\">\n<p style=\"text-align:left;text-align:right;direction:rtl\"> <strong>\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646<\/strong> \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8087bb711e716aca4a2c535eaeb8b0bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( a+b\\right)^n = &amp; \\sum_{k=0}^{n}\\begin{pmatrix} n\\\\ k\\end{pmatrix}a^{n-k}b^k\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"204\" style=\"vertical-align: -22px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648 \u0645\u0627 \u064a\u0639\u0627\u062f\u0644\u0647\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19bab1dcab88a71b5b3bed39bf09cc73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( a+b\\right)^n =\\begin{pmatrix} n \\\\ 0 \\end{pmatrix} \\right)a^n b^0 + \\begin{pmatrix} n \\\\ 1 \\end{pmatrix} a^{n-1}b^{1} + \\begin{pmatrix} n \\\\ 2 \\end{pmatrix} a^{n-2}b^{2} + \\dots + \\begin{pmatrix} n \\\\ n \\end{pmatrix} a^0 b^{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"520\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0635\u064a\u063a\u0629 \u0645\u0639\u0642\u062f\u0629 \u0628\u0639\u0636 \u0627\u0644\u0634\u064a\u0621 \u0644\u0641\u0647\u0645 \u0645\u0641\u0647\u0648\u0645 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u0644\u0630\u0644\u0643 \u0642\u0645\u0646\u0627 \u0628\u0639\u0631\u0636 \u0642\u0648\u0649 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0646 \u0623\u062f\u0646\u0649 \u062f\u0631\u062c\u0629 \u0623\u062f\u0646\u0627\u0647 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0641\u0647\u0645\u0647\u0627 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-binomiale-ou-theoreme-de-newton.jpg\" alt=\"\u0635\u064a\u063a\u0629 \u0644\u0646\u0638\u0631\u064a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646\" class=\"wp-image-2126\" width=\"578\" height=\"578\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u0639\u0646\u062f \u062a\u0648\u0633\u064a\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 <strong>\u060c \u062a\u0646\u062e\u0641\u0636 \u0623\u0633\u0633 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 (\u0623)<\/strong> \u0628\u064a\u0646\u0645\u0627 <strong>\u062a\u0632\u062f\u0627\u062f \u0623\u0633\u0633 \u0627\u0644\u062d\u062f \u0627\u0644\u062b\u0627\u0646\u064a (\u0628)<\/strong> \u060c \u062a\u0645\u0627\u0645\u064b\u0627 \u0643\u0645\u0627 \u064a\u0632\u064a\u062f \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0623\u062f\u0646\u0649 \u0641\u064a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0645\u0639\u0631\u0641\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0631\u0642\u0645 \u0627\u0646\u062f\u0645\u0627\u062c\u064a\u060c \u0623\u064a \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u0628\u0631\u064a \u0645\u0646 \u0627\u0644\u0646\u0648\u0639<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-59b5fcabfa89714b1a55cbd237e405ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 4 \\\\ 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"29\" style=\"vertical-align: -17px;\"><\/p>\n<p> . \u0644\u0630\u0644\u0643\u060c \u0642\u0628\u0644 \u0623\u0646 \u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0623\u0645\u062b\u0644\u0629 \u062d\u0648\u0644 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0627\u062c\u0639 \u0628\u0625\u064a\u062c\u0627\u0632 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Numero-combinatorio\"><\/span> \u0631\u0642\u0645 \u0627\u0646\u062f\u0645\u0627\u062c\u064a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u062a\u062d\u062f\u064a\u062f <strong>\u0631\u0642\u0645 \u0627\u0646\u062f\u0645\u0627\u062c\u064a<\/strong> (\u0623\u0648 \u0645\u0639\u0627\u0645\u0644 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646) \u064a\u062c\u0628 \u0639\u0644\u064a\u0643 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b0b6e9d4f65b3670d26dabb0141b15fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}n \\\\ k \\end{pmatrix} = \\cfrac{n!}{k!(n-k)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"135\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0630\u0647\u0628<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da0ef996f36e1b32a0f26f6e896e1771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n!\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ef344500b3e227ba2eebac8f79f8229a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k!\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0647\u0630\u0647 <strong>\u0623\u0631\u0642\u0627\u0645 \u0639\u0627\u0645\u0644\u064a\u0629<\/strong> . \u062f\u0639\u0648\u0646\u0627 \u0646\u062a\u0630\u0643\u0631 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646\u0647 \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0642\u0645 \u0627\u0644\u0636\u0631\u0628\u064a \u0639\u0646 \u0637\u0631\u064a\u0642 \u0636\u0631\u0628 \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0627\u0644\u0645\u0648\u062c\u0628\u0629 \u0644\u0644\u0640 1 \u0641\u064a \u0627\u0644\u0631\u0642\u0645 \u0627\u0644\u0645\u0630\u0643\u0648\u0631:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-09df3296b34c0da43f17d367af376ce5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! = 1 \\cdot 2 \\cdot 3 \\cdots (n-1) \\cdot n\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0646\u062c\u062f \u0631\u0642\u0645\u064b\u0627 \u0627\u0646\u062f\u0645\u0627\u062c\u064a\u064b\u0627 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0631\u0624\u064a\u0629 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-619109bf5a34808b1f72ef6799a75482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 4\\\\ 3 \\end{pmatrix} = \\cfrac{4!}{3!(4-3)!}=\\cfrac{4!}{3!\\cdot 1!}= \\cfrac{1 \\cdot 2\\cdot 3 \\cdot 4}{(1 \\cdot 2\\cdot 3) \\cdot 1} = \\cfrac{24}{6} = 4\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"385\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0639\u0628\u0631 \u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0641\u062a\u0627\u062d <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-840c7e15e97f9fa0c5615b063966e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{nCr}.\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"48\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Ejemplos-del-binomio-de-Newton\"><\/span> \u0646\u064a\u0648\u062a\u0646 \u0623\u0645\u062b\u0644\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0628\u0639\u062f \u0623\u0646 \u0639\u0631\u0641\u0646\u0627 \u0645\u0627 \u0647\u064a \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0627\u0644\u064a\u0646 \u0639\u062f\u062f\u064a\u064a\u0646.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 1<\/h3>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0637\u0628\u0651\u0642 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0644\u062d\u0633\u0627\u0628 \u0642\u0648\u0629 \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-765733b5fff1862758f20d820c234683_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+3)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0627\u0644\u0648\u0627\u0636\u062d \u0623\u0646\u0647 \u0628\u0645\u0627 \u0623\u0646 \u0647\u0630\u0647 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0628\u0639\u0629\u060c \u0641\u064a\u0645\u0643\u0646 \u062d\u0644\u0647\u0627 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a \u0627\u0644\u0645\u062a\u0637\u0627\u0628\u0642\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0632\u0629 ( <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0627\u0644\u0647\u0648\u064a\u0627\u062a-\u0627\u0644\u0645\u0646\u062a\u062c\u0627\u062a-\u0627\u0644\u0645\u0633\u0627\u0648\u0627\u0629-\u0627\u0644\u0628\u0627\u0631\u0632\u0629-\u062a\u0645\u0627\u0631\u064a\u0646-\u0645\u062d\u0644\u0648\u0644\u0629\/\">\u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0627\u0644\u0645\u062a\u0637\u0627\u0628\u0642\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0632\u0629<\/a><\/span><\/strong> )\u060c \u0644\u0643\u0646\u0646\u0627 \u0633\u0646\u062d\u0633\u0628\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0643\u0645\u062b\u0627\u0644.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19bab1dcab88a71b5b3bed39bf09cc73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( a+b\\right)^n =\\begin{pmatrix} n \\\\ 0 \\end{pmatrix} \\right)a^n b^0 + \\begin{pmatrix} n \\\\ 1 \\end{pmatrix} a^{n-1}b^{1} + \\begin{pmatrix} n \\\\ 2 \\end{pmatrix} a^{n-2}b^{2} + \\dots + \\begin{pmatrix} n \\\\ n \\end{pmatrix} a^0 b^{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"520\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0646 = 2\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e75e12f24582b099635b2287594fbd00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =\\begin{pmatrix} 2 \\\\ 0 \\end{pmatrix} \\right)x^2 \\cdot 3^0 + \\begin{pmatrix} 2 \\\\ 1 \\end{pmatrix} x^1\\cdot3^1 + \\begin{pmatrix} 2 \\\\ 2 \\end{pmatrix} x^{0}\\cdot3^{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"383\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0646\u0638\u0631 \u062c\u064a\u062f\u0627\u064b\u060c \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629 \u0646\u0631\u0641\u0639 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 (x) \u0625\u0644\u0649 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0642\u0635\u0649 \u0627\u0644\u0645\u0645\u0643\u0646\u060c \u0648\u0647\u0648 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0647\u0648 2. \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0646\u0631\u0641\u0639 \u0627\u0644\u062d\u062f \u0627\u0644\u062b\u0627\u0646\u064a (3) \u0625\u0644\u0649 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 \u0627\u0644\u0645\u0645\u0643\u0646\u060c \u0648\u0647\u0648 \u062f\u0627\u0626\u0645\u0627\u064b 0. \u0644\u0643\u0646 \u0639\u0646\u062f\u0645\u0627 \u0646\u062a\u062c\u0647 \u0625\u0644\u0649 \u0627\u0644\u064a\u0645\u064a\u0646\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0631\u0641\u0639 <strong>\u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 \u0625\u0644\u0649 \u0631\u0642\u0645 \u0623\u0642\u0644 \u0645\u0646 \u0627\u0644\u0633\u0627\u0628\u0642<\/strong> \u0648\u0627\u0644\u062d\u062f <strong>\u0627\u0644\u062b\u0627\u0646\u064a \u0625\u0644\u0649 \u0631\u0642\u0645 \u0623\u0639\u0644\u0649 \u0645\u0646 \u0627\u0644\u0633\u0627\u0628\u0642.<\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u062f\u0639\u0648\u0646\u0627 \u0646\u062d\u0633\u0628 \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-541c34c91eb3c95f11be4b0e19a9a882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =1\\cdot x^2\\cdot 3^0 + 2\\cdot x^1\\cdot 3^1 + 1\\cdot x^{0}\\cdot 3^{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"334\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0646 \u0646\u062d\u0644 \u0644\u0644\u0642\u0648\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ba9ed22a3248d243b7298f36be657c7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =1\\cdot x^2\\cdot 1 + 2\\cdot x\\cdot 3 + 1\\cdot 1\\cdot 9\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"295\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062d\u0633\u0628 \u0627\u0644\u0636\u0631\u0628:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d43c304356e20edd6c9b63e0703a279f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( x+3\\right)^2 =x^2 + 6x + 9\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"174\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0633\u0646\u0642\u0648\u0645 \u0628\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0623\u0643\u062b\u0631 \u0635\u0639\u0648\u0628\u0629 \u0642\u0644\u064a\u0644\u0627\u064b.<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0642\u0645 \u0628\u062a\u0637\u0628\u064a\u0642 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0625\u064a\u062c\u0627\u062f \u0642\u0648\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5466a47ebcb4446937988adabd0c64f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x+1)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0635\u064a\u063a\u0629 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0647\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-19bab1dcab88a71b5b3bed39bf09cc73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( a+b\\right)^n =\\begin{pmatrix} n \\\\ 0 \\end{pmatrix} \\right)a^n b^0 + \\begin{pmatrix} n \\\\ 1 \\end{pmatrix} a^{n-1}b^{1} + \\begin{pmatrix} n \\\\ 2 \\end{pmatrix} a^{n-2}b^{2} + \\dots + \\begin{pmatrix} n \\\\ n \\end{pmatrix} a^0 b^{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"520\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0646 = 3\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e55cd40782bdb46907860c3e04c49fbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} \\right)(2x)^3 \\cdot 1^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} (2x)^{2}\\cdot 1^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} (2x)^{1}\\cdot 1^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} (2x)^{0}\\cdot 1^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"589\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7ff5e4d9ee6990d854f22059f7db0d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =1\\cdot (2x)^3 \\cdot 1^0 + 3\\cdot (2x)^{2}\\cdot 1^1 + 3 \\cdot (2x)^{1}\\cdot 1^{2} + 1\\cdot (2x)^{0}\\cdot 1^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"524\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u062d\u0644 \u0627\u0644\u0642\u0648\u0649\u060c \u0644\u0630\u0644\u0643 \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u0623\u0646 \u062a\u062a\u0630\u0643\u0631 \u0627\u0644\u062e\u0627\u0635\u064a\u062a\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u062a\u064a\u0646:<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7;text-align:right;direction:rtl\"> \u2022 \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u0631\u0641\u0639 \u0648\u062d\u064a\u062f\u0629 \u0627\u0644\u062d\u062f \u0625\u0644\u0649 \u0627\u0644\u0623\u0633\u060c \u064a\u062a\u0645 \u0631\u0641\u0639 \u0627\u0644\u0645\u0639\u0627\u0645\u0644 \u0648\u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0625\u0644\u0649 \u0646\u0641\u0633 \u0627\u0644\u0623\u0633 \u2192<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3426c618ed82b8baf60f97603a2e17f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x)^3=2^3\\cdot x^3 =8\\cdot x^3 =8x^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"223\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u2022 \u0623\u064a \u062d\u062f \u064a\u0635\u0644 \u0625\u0644\u0649 0 \u064a\u0639\u0637\u064a 1 \u2192<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cdfedc209dec05e7c24c7b35478e795b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x)^0=1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u0646\u062c\u062f \u0627\u0644\u0642\u0648\u0649 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0627\u062a\u064a\u0646 \u0627\u0644\u062e\u0627\u0635\u064a\u062a\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-97b81539ae095cd73e1054b74e5fe5c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =1\\cdot 2^3x^3 \\cdot 1 + 3\\cdot 2^2x^{2}\\cdot 1 + 3 \\cdot 2^1x^{1}\\cdot 1 + 1\\cdot 1\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"443\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-825eca438cd77124fb64e987aef09e39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =1\\cdot 8x^3 \\cdot 1 + 3\\cdot 4x^{2}\\cdot 1 + 3 \\cdot 2x\\cdot 1 + 1\\cdot 1\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"412\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u0636\u0631\u0628 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d666ed4bb3a25b85121e7b8be0e7295e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left( 2x+1\\right)^3 =8x^3 + 12x^{2}+6x + 1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"248\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"El-binomio-de-Newton-y-el-triangulo-de-Tartaglia-o-de-Pascal\"><\/span> \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0648\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644).<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u0631\u0623\u064a\u062a \u0641\u064a \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0623\u0639\u0644\u0627\u0647\u060c \u0641\u0625\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0623\u0645\u0631 \u0645\u0645\u0644 \u0628\u0639\u0636 \u0627\u0644\u0634\u064a\u0621. \u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628\u060c \u0633\u0646\u0639\u0644\u0645\u0643 \u062e\u062f\u0639\u0629 \u062d\u062a\u0649 \u0644\u0627 \u062a\u0636\u0637\u0631 \u0625\u0644\u0649 \u062d\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629\u060c \u062d\u064a\u062b \u064a\u0645\u0643\u0646\u0643 \u0645\u0639\u0631\u0641\u0629 \u0642\u064a\u0645\u062a\u0647\u0627 \u0645\u0628\u0627\u0634\u0631\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627\u060c \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0633\u0645 \u0645\u062b\u0644\u062b \u0628\u0627\u0633\u0643\u0627\u0644.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0641\u064a \u062d\u0627\u0644 \u0643\u0646\u062a \u0644\u0627 \u062a\u0639\u0631\u0641 \u0645\u0627 \u0647\u0648\u060c <strong>\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u063a\u0644\u064a\u0627<\/strong> \u060c \u0648\u064a\u0633\u0645\u0649 \u0623\u064a\u0636\u064b\u0627 <strong>\u0645\u062b\u0644\u062b \u0628\u0627\u0633\u0643\u0627\u0644<\/strong> \u060c \u0647\u0648 \u062a\u0645\u062b\u064a\u0644 \u0631\u064a\u0627\u0636\u064a \u0644\u0644\u0623\u0631\u0642\u0627\u0645 \u0645\u0631\u062a\u0628\u0629 \u0641\u064a \u0634\u0643\u0644 \u0645\u062b\u0644\u062b.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0628\u0646\u0627\u0621 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 \u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644 \u064a\u062c\u0628 \u0623\u0646 \u0646\u0628\u062f\u0623 \u0645\u0646 \u0642\u0645\u0629 \u0627\u0644\u0645\u062b\u0644\u062b \u0648\u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u0627 1\u060c \u0648\u0645\u0646 \u062b\u0645 \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0623\u062f\u0646\u0627\u0647. \u0643\u0644 \u0631\u0642\u0645 \u0641\u064a \u0627\u0644\u0633\u0637\u0648\u0631 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u064a\u0633\u0627\u0648\u064a \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0631\u0642\u0645\u064a\u0646 \u0627\u0644\u0644\u0630\u064a\u0646 \u0641\u0648\u0642\u0647 \u0645\u0628\u0627\u0634\u0631\u0629\u060c \u0645\u0627 \u0639\u062f\u0627 \u0646\u0647\u0627\u064a\u062a\u064a \u0627\u0644\u0633\u0637\u0648\u0631 \u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 1. <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/comment-construire-le-triangle-tartaglia-de-pascal.jpg\" alt=\"\u0646\u064a\u0648\u062a\u0646 \u0632\u0648\u062c 1 \u0627\u0644\u0645\u062f\u0631\u0633\u0629 \u0627\u0644\u062b\u0627\u0646\u0648\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0627\u0646\u062a\u0631\u0646\u062a\" class=\"wp-image-1936\" width=\"220\" height=\"288\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0646\u060c \u0643\u0644 \u0631\u0642\u0645 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0641\u064a \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 \u064a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639 \u0646\u062a\u064a\u062c\u0629 \u0631\u0642\u0645 \u0627\u0646\u062f\u0645\u0627\u062c\u064a\u060c \u0627\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u062a\u0627\u0644\u064a: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/tirangulo-de-tartaglia-pascal-nombres-combinatoires.jpg\" alt=\"\" class=\"wp-image-1969\" width=\"538\" height=\"204\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0645\u0639\u0627\u0645\u0644 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b9c97b98e22e9867a562555c1a3db2d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"29\" style=\"vertical-align: -17px;\"><\/p>\n<p> \u064a\u0639\u0627\u062f\u0644 3\u060c \u0644\u0623\u0646\u0647 \u0641\u064a \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 \u064a\u0648\u062c\u062f 3 \u0641\u064a \u0645\u0648\u0636\u0639\u0647.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u063a\u0644\u064a\u0627 (\u0623\u0648 \u0645\u062b\u0644\u062b \u0628\u0627\u0633\u0643\u0627\u0644) \u0644\u062d\u0644 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0628\u0633\u0631\u0639\u0629 \u0623\u0643\u0628\u0631 \u0628\u0643\u062b\u064a\u0631\u060c \u0644\u0623\u0646\u0647 \u064a\u0648\u0641\u0631 \u0639\u0644\u064a\u0646\u0627 \u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0625\u0630\u0627 \u0623\u0631\u062f\u0646\u0627 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062a\u0639\u0632\u064a\u0632 \u0627\u0644\u062a\u0627\u0644\u064a \u0644\u0642\u064a\u0645\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ebc694e191c443617943252538d68669_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+5)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u062a\u0637\u0628\u064a\u0642 \u0642\u0627\u0639\u062f\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u0628\u0631\u064a \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c519ee24ca58f3139893d7350189527f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} \\right)x^3 \\cdot 5^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} x^{2}\\cdot 5^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} x^{1}\\cdot 5^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} x^{0}\\cdot 5^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"490\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0633\u0646\u064b\u0627\u060c \u0628\u062f\u0644\u064b\u0627 \u0645\u0646 \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0627\u0646\u062f\u0645\u0627\u062c\u064a\u0629 \u0648\u0627\u062d\u062f\u064b\u0627 \u062a\u0644\u0648 \u0627\u0644\u0622\u062e\u0631\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0628\u0628\u0633\u0627\u0637\u0629 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0643\u0644 \u0631\u0642\u0645 \u0627\u0646\u062f\u0645\u0627\u062c\u064a \u0628\u0645\u0639\u0627\u0645\u0644\u0647 \u0627\u0644\u0645\u0642\u0627\u0628\u0644 \u0641\u064a \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u064a\u062a\u0645 \u0631\u0641\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0644\u062b\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0647\u064a \u062a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0644\u062b \u0644\u0644\u0645\u062b\u0644\u062b: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u062c\u0644\u064a\u0627 \u0623\u0648 \u0645\u062b\u0644\u062b \u0628\u0627\u0633\u0643\u0627\u0644 \u0648\u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\" class=\"wp-image-2041\" width=\"319\" height=\"218\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-137ba158b5fc348259d802391c34dfad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =\\color{red} \\bm{1} \\color{black} \\cdot x^3 \\cdot 5^0 + \\color{red} \\bm{3} \\color{black}  \\cdot x^{2}\\cdot 5^1 + \\color{red} \\bm{3} \\color{black} \\cdot x^{1}\\cdot 5^{2} +\\color{red} \\bm{1} \\color{black} \\cdot x^{0}\\cdot 5^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"582\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0622\u0646 \u0643\u0644 \u0645\u0627 \u0639\u0644\u064a\u0646\u0627 \u0641\u0639\u0644\u0647 \u0647\u0648 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0628\u0642\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-baa8da36add688734cd5c35e495e6326_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =1 \\cdot x^3 \\cdot 1 + 3\\cdot  x^{2}\\cdot 5 + 3 \\cdot x\\cdot 25 +1\\cdot 1\\cdot 125\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"404\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc2cf49b9bd743a6f47bde4ca0646b39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+5\\right)^3 =x^3+ 15x^2 + 75x +125\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"257\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0643\u0645\u0627 \u062a\u0631\u0648\u0646\u060c \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644) \u0644\u062d\u0633\u0627\u0628 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0628\u0637\u0631\u064a\u0642\u0629 \u0623\u0628\u0633\u0637 \u0648\u0623\u0633\u0631\u0639\u060c \u0643\u0645\u0627 \u0623\u0638\u0647\u0631\u0646\u0627. \u0648\u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628 \u0646\u0648\u0635\u064a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647.<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0644\u062a\u0644\u062e\u064a\u0635 \u0643\u0644 \u0645\u0627 \u0631\u0623\u064a\u0646\u0627\u0647 \u062d\u062a\u0649 \u0627\u0644\u0622\u0646\u060c \u0646\u062a\u0631\u0643\u0643\u0645 \u0645\u0639 \u0635\u0648\u0631\u0629 \u062a\u0648\u0636\u062d \u0643\u064a\u0641 \u062a\u0628\u062f\u0648 \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0645\u0639 \u0623\u0631\u0642\u0627\u0645 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644): <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/binome-de-newton-et-triangle-de-pascal-ou-de-tartaglia-2.jpg\" alt=\"\u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0648\u0645\u062b\u0644\u062b \u0628\u0627\u0633\u0643\u0627\u0644 \u0623\u0648 \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627\" class=\"wp-image-2151\" width=\"535\" height=\"379\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Binomio-de-Newton-negativo-potencia-de-una-resta\"><\/span> \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0644\u0646\u064a\u0648\u062a\u0646: \u0642\u0648\u0629 \u0627\u0644\u0637\u0631\u062d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u062a\u0649 \u0627\u0644\u0622\u0646\u060c \u062c\u0645\u064a\u0639 \u0623\u0645\u062b\u0644\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0627\u0644\u062a\u064a \u0642\u0645\u0646\u0627 \u0628\u062d\u0644\u0647\u0627 \u0643\u0627\u0646\u062a \u0645\u062c\u0631\u062f \u0625\u0636\u0627\u0641\u0627\u062a. \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0644\u0623\u062d\u062f \u062d\u062f\u064a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0639\u0644\u0627\u0645\u0629 \u0633\u0644\u0628\u064a\u0629\u060c \u064a\u0638\u0644 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0645\u0634\u0627\u0628\u0647\u064b\u0627 \u0648\u0644\u0643\u0646\u0647 \u064a\u062a\u063a\u064a\u0631 \u0642\u0644\u064a\u0644\u0627\u064b.<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee;text-align:right;direction:rtl\"> \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0623\u062d\u062f \u062d\u062f\u0648\u062f \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0633\u0627\u0644\u0628\u064b\u0627\u060c \u0623\u064a \u0623\u0646\u0647 \u0637\u0631\u062d \u0645\u0646 \u0627\u0644\u0646\u0648\u0639 (ab) <sup>n<\/sup> \u060c \u0641\u0625\u0646 \u0639\u0644\u0627\u0645\u0627\u062a \u0645\u0641\u0643\u0648\u0643 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u064a\u062c\u0628 \u0623\u0646 \u062a\u062a\u0646\u0627\u0648\u0628 \u0639\u0644\u0649 \u0627\u0644\u0635\u0648\u0631\u0629 + \u2013 + \u2013 + \u2013 + \u2013 \u2026<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0642\u0645\u0646\u0627 \u0623\u062f\u0646\u0627\u0647 \u0628\u062a\u0637\u0648\u064a\u0631 \u0642\u0648\u0649 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u0644\u0644\u062f\u0631\u062c\u0627\u062a \u0627\u0644\u062e\u0645\u0633 \u0627\u0644\u0623\u0648\u0644\u0649 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0648\u0645\u0639 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0628\u0627\u0644\u0641\u0639\u0644\u060c \u0628\u062d\u064a\u062b \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0639\u062b\u0648\u0631 \u0645\u0628\u0627\u0634\u0631\u0629 \u0639\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u0630\u064a \u062a\u062d\u062a\u0627\u062c\u0647: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/puissance-binomiale-newton-negative-dune-soustraction-2.jpg\" alt=\"\u0642\u0648\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u0633\u0644\u0628\u064a\u0629 \u0644\u0644\u0637\u0631\u062d 2\" class=\"wp-image-2147\" width=\"525\" height=\"387\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Propiedades-del-binomio-de-Newton\"><\/span> \u062e\u0635\u0627\u0626\u0635 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062a\u0645\u064a\u0632 \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0628\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u064a\u0624\u062f\u064a \u062a\u062d\u0644\u064a\u0644 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0625\u0644\u0649 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062d\u062f \u0648\u0627\u062d\u062f \u0623\u0643\u0628\u0631 \u0645\u0646 \u062f\u0631\u062c\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646. \u0623\u0648 \u0628\u0645\u0639\u0646\u0649 \u0622\u062e\u0631 \u0644\u0644\u0632\u0648\u062c\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a7cb070eb92ff2ce3199cbbf72ab6122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^n\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"60\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0644\u0642\u062f \u062a\u0623\u062b\u0631\u0648\u0627<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d72f4e3699652cfc70b8880515893d7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n+1\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"40\" style=\"vertical-align: -2px;\"><\/p>\n<p> \u0634\u0631\u0648\u0637.<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0635\u0644\u0627\u062d\u064a\u0627\u062a \u0627\u0644\u0639\u0646\u0635\u0631\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0623\u0628\u062f\u0627 \u0628<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648\u062a\u0646\u062e\u0641\u0636 \u062d\u062a\u0649 \u062a\u0635\u0644 \u0625\u0644\u0649 0 \u0641\u064a \u0627\u0644\u0631\u0628\u0639 \u0627\u0644\u0623\u062e\u064a\u0631.<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0635\u0644\u0627\u062d\u064a\u0627\u062a \u0627\u0644\u0639\u0646\u0635\u0631\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u064a\u0630\u0647\u0628\u0648\u0646 \u0641\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0627\u0644\u0622\u062e\u0631: \u064a\u0628\u062f\u0623\u0648\u0646 \u0645\u0646 0 \u0648\u064a\u0632\u062f\u0627\u062f\u0648\u0646 \u062d\u062a\u0649 \u064a\u0635\u0644\u0648\u0627<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0641\u064a \u0627\u0644\u0641\u0635\u0644 \u0627\u0644\u0623\u062e\u064a\u0631.<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0644\u0643\u0644 \u0639\u0646\u0635\u0631 \u0645\u0646 \u0639\u0646\u0627\u0635\u0631 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0623\u0633\u0633\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0648<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u0645\u0633\u0627\u0648\u064a \u0644<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7ecab3f5df4767e23a2660ceb88ceabd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 \u0645\u0646 \u062a\u0639\u0628\u064a\u0631 \u0646\u064a\u0648\u062a\u0646 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646 \u0647\u0648 \u062f\u0627\u0626\u0645\u064b\u0627 1 (\u0645\u0648\u062c\u0628) \u0648\u0627\u0644\u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u062b\u0627\u0646\u064a \u064a\u0639\u0627\u062f\u0644 \u0623\u0633 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0645\u0648\u062c\u0628 \u0623\u0648 \u0633\u0627\u0644\u0628). <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Calcular-el-termino-k-esimo-del-binomio-de-Newton\"><\/span> \u0627\u062d\u0633\u0628 \u0627\u0644\u062d\u062f k \u0645\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0647\u0630\u0627 \u0623\u0645\u0631 \u063a\u064a\u0631 \u0645\u0639\u062a\u0627\u062f\u060c \u0625\u0644\u0627 \u0623\u0646\u0646\u0627 \u0642\u062f \u0646\u0648\u0627\u062c\u0647 \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u0645\u0634\u0643\u0644\u0627\u062a\u060c \u062d\u064a\u062b \u064a\u064f\u0637\u0644\u0628 \u0645\u0646\u0627\u060c \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u062a\u0648\u0633\u064a\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u062d\u062f k \u0645\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u0623\u064a \u0627\u0644\u062d\u062f \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0644 \u0627\u0644\u0645\u0648\u0636\u0639 k.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u062d\u062f \u0627\u0644\u0630\u064a \u064a\u0634\u063a\u0644 \u0627\u0644\u0645\u0643\u0627\u0646 k \u0641\u064a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0625\u0636\u0627\u0641\u0629 \u0623\u0648 \u0637\u0631\u062d:<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;;text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0645\u0648\u062c\u0628\u0629\u060c \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0642\u064a\u0645\u0629 \u0627\u0644\u062d\u062f k \u0628\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-935aea7ee9ad482a391d2383ce37721b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^n \\quad \\color{red} \\bm{\\longrightarrow} \\color{black} \\quad T_k = \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1}b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"389\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;;text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color:#000000;font-weight: normal;\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0633\u0627\u0644\u0628\u0629\u060c \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0642\u064a\u0645\u0629 \u0627\u0644\u062d\u062f k \u0628\u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e47024f65b665936296385eae56276af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^n \\quad \\color{red} \\bm{\\longrightarrow} \\color{black} \\quad T_k = (-1)^{k-1} \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1} b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"454\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0646\u062c\u062f \u0627\u0644\u062d\u062f \u0627\u0644\u0631\u0627\u0628\u0639 \u0645\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 5 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c380d61c29b21a0e902b38e390bab73b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+3)^5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0645\u0627 \u0623\u0646\u0647\u0627 \u0630\u0627\u062a \u062d\u062f\u064a\u0646 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0637\u0628\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0623\u0648\u0644\u0649:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88faab054915aad2321276aca8b42244_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_k = \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1}b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"198\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u0628\u062f\u0644 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629 \u0628\u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0644\u0647\u0627:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b3b33ca71b5d419c83bb4c5c4b399a69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = \\begin{pmatrix} 5 \\\\ 4-1 \\end{pmatrix} x^{5-4+1}\\cdot 3^{4-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"209\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0646\u0642\u0648\u0645 \u0628\u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9dbb0f95e11df6bb989c1a296d168d06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = \\begin{pmatrix} 5 \\\\ 3 \\end{pmatrix} x^{2}\\cdot 3^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"126\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d566482a87af0eea361c2d7fb816376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = 10 \\cdot x^{2}\\cdot 27\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9159bbe88a83e38918e8b26354c51db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_4 = 270 x^{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"86\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0646\u0643\u0648\u0646 \u0642\u062f \u062d\u0633\u0628\u0646\u0627 \u0627\u0644\u062d\u062f \u0627\u0644\u0631\u0627\u0628\u0639 \u0645\u0646 \u0645\u0641\u0643\u0648\u0643 \u0646\u064a\u0648\u062a\u0646 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u062f\u0648\u0646 \u0627\u0644\u062d\u0627\u062c\u0629 \u0625\u0644\u0649 \u062d\u0633\u0627\u0628 \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0623\u062e\u0631\u0649. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-binomio-de-Newton\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0639\u0644\u0649 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0628\u0639\u062f \u0623\u0646 \u0634\u0631\u062d\u0646\u0627 \u0645\u0627 \u0647\u064a \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u0646\u062a\u0631\u0643\u0643 \u0645\u0639 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u062d\u0648\u0644 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627. \u062a\u0630\u0643\u0631 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646\u0647 \u064a\u0645\u0643\u0646\u0643 \u062a\u0631\u0643 \u0623\u064a \u0623\u0633\u0626\u0644\u0629 \u0623\u0648 \u0627\u0642\u062a\u0631\u0627\u062d\u0627\u062a \u0644\u0646\u0627 \u0641\u064a \u0627\u0644\u062a\u0639\u0644\u064a\u0642\u0627\u062a.<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 1<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0642\u0645 \u0628\u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0642\u0648\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a303d8317c1cf803d486406be48ca672_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+4)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0633\u062a\u062e\u062f\u0645 \u0623\u0648\u0644\u0627\u064b \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-34471d980abe3399791b053ae6b92949_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(x+4\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} x^3 \\cdot 4^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} x^{2}\\cdot 4^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} x^{1}\\cdot 4^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} x^{0}\\cdot 4^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"490\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0627 \u0623\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u0629 \u0644\u0644\u0642\u0648\u0629 3\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0644\u062b \u0644\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 \u0644\u0644\u0639\u062b\u0648\u0631 \u0645\u0628\u0627\u0634\u0631\u0629 \u0639\u0644\u0649 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u062a\u0645\u0627\u0631\u064a\u0646 \u0639\u0644\u0649 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 1 \u062b\u0627\u0646\u0648\u064a\u0629 \u0639\u0627\u0645\u0629\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8a4212d723eba76e9d883827da60cbfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+4)^3 =  1\\cdot x^3 \\cdot 4^0+3 \\cdot x^2 \\cdot 4^1 + 3 \\cdot x^1 \\cdot 4^2+1 \\cdot x^0 \\cdot 4^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"425\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0635\u0644\u0627\u062d\u064a\u0627\u062a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f263aaef5f957165f9d251d4d129038a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot x^3 \\cdot 1 + 3 \\cdot x^2 \\cdot 4+ 3 \\cdot x \\cdot 16 +1 \\cdot 1 \\cdot 64\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"310\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627 \u0646\u0636\u0631\u0628: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dce7abd76ef03c986508c67f59ed4065_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3  + 3x^2 \\cdot 4 + 3 x \\cdot 16 + 64\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"199\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c0e5d024d22382b1b37a5123547bca3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x^3  + 12x^2  + 48 x + 64}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"164\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u062a\u0645\u0631\u064a\u0646 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2a2d15ee45a0d9497294d2d4c96b59c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3x+2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627\u060c \u0646\u0637\u0628\u0642 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-11acde04483aaa747da0acd16b4912f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle  \\left(3x+2\\right)^3 =\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} (3x)^3 \\cdot 2^0 + \\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} (3x)^{2}\\cdot 2^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} (3x)^{1}\\cdot 2^{2} + \\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} (3x)^{0}\\cdot 2^{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"589\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0645\u0627 \u0623\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0643\u0639\u0628\u0629\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0644\u062b \u0644\u0645\u062b\u0644\u062b \u0628\u0627\u0633\u0643\u0627\u0644 \u0644\u0645\u0639\u0631\u0641\u0629 \u0642\u064a\u0645 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0628\u0634\u0643\u0644 \u0645\u0628\u0627\u0634\u0631: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u062a\u0645\u0627\u0631\u064a\u0646 \u0639\u0644\u0649 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 1 \u062b\u0627\u0646\u0648\u064a\u0629 \u0639\u0627\u0645\u0629\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9086d7be80cd0ba60f0733f2c3a6d042_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left(3x+2\\right)^3 =  1\\cdot  (3x)^3 \\cdot 2^0+3 \\cdot (3x)^2 \\cdot 2^1+ 3 \\cdot (3x)^1 \\cdot 2^2+1 \\cdot (3x)^0 \\cdot 2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"524\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u0642\u0648\u0649 \u0623\u062d\u0627\u062f\u064a\u0627\u062a \u0627\u0644\u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2db17751cff5427aa6a3f5da817ba4d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot  27x^3 \\cdot 1+ 3 \\cdot 9x^2 \\cdot 2+3 \\cdot 3x \\cdot 4 + 1 \\cdot 1 \\cdot 8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"328\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627 \u0646\u0642\u0648\u0645 \u0628\u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u0636\u0631\u0628: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-92736e691facfdd97f2107b4451b5d07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"27x^3  + 27x^2 \\cdot 2 +9x \\cdot 4+8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"207\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-498bf09ef09e1b2585a5a01193eb94d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{27x^3  + 54x^2  +36x+8}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"173\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0642\u0645 \u0628\u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad4da49317f5a667d4f0402b064911cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644\u0627\u060c \u0646\u0633\u062a\u062e\u062f\u0645 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646. \u0644\u0643\u0646 \u0628\u0645\u0627 \u0623\u0646 \u0644\u062f\u064a\u0646\u0627 \u0639\u0645\u0644\u064a\u0629 \u0637\u0631\u062d \u062f\u0627\u062e\u0644 \u0627\u0644\u0642\u0648\u0633\u064a\u0646\u060c \u0641\u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0628\u062f\u064a\u0644 \u0639\u0644\u0627\u0645\u0627\u062a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0643\u0644 \u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6515c9dadfa92cfcc27393786b322d8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-2)^3=\\begin{pmatrix} 3 \\\\ 0 \\end{pmatrix} (2x)^3 \\cdot 2^0-\\begin{pmatrix} 3 \\\\ 1 \\end{pmatrix} (2x)^2 \\cdot 2^1 + \\begin{pmatrix} 3 \\\\ 2 \\end{pmatrix} (2x)^1 \\cdot 2^2-\\begin{pmatrix} 3 \\\\ 3 \\end{pmatrix} (2x)^0 \\cdot 2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"589\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0627 \u0623\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u0629 \u0644\u0644\u0642\u0648\u0629 \u062b\u0644\u0627\u062b\u0629\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u062b\u0627\u0644\u062b \u0644\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629 \u0645\u0628\u0627\u0634\u0631\u0629: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-de-tartaglia-et-binome-de-newton-ou-pascal.png\" alt=\"\u062a\u0645\u0627\u0631\u064a\u0646 \u0639\u0644\u0649 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 1 \u062b\u0627\u0646\u0648\u064a\u0629 \u0639\u0627\u0645\u0629\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d6210b9c330fe976b32741ba8d94682_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-2)^3=1\\cdot  (2x)^3 \\cdot 2^0-3 \\cdot (2x)^2 \\cdot 2^1 + 3 \\cdot (2x)^1 \\cdot 2^2-1 \\cdot (2x)^0 \\cdot 2^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"524\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0635\u0644\u0627\u062d\u064a\u0627\u062a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25d9bc802e8f03513de309b82066a983_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot  8x^3 \\cdot 1- 3 \\cdot 4 x^2 \\cdot 2+ 3 \\cdot 2x \\cdot 4-1 \\cdot 1 \\cdot 8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"319\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u062d\u0644 \u0627\u0644\u0636\u0631\u0628: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5534981aec0ef30054d35f3dd9d9779d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"8x^3  - 12 x^2 \\cdot 2 +6x \\cdot 4 -8\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"199\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-be12e609798d32d7b7c84bae80e04236_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{8x^3  -24 x^2  +24x -8}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"164\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0645\u0648\u0633\u0639 \u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0646\u064a\u0648\u062a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6fc4cfe6afa91b302683d9891d785376_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(4x-3y)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"79\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u0648\u0644\u0643\u0646 \u0643\u0645\u0627 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0644\u062f\u064a\u0646\u0627 \u0639\u0645\u0644\u064a\u0629 \u0637\u0631\u062d \u0628\u064a\u0646 \u0642\u0648\u0633\u064a\u0646\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u062a\u0628\u062f\u064a\u0644 \u0639\u0644\u0627\u0645\u0627\u062a \u0643\u0644 \u062d\u062f:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7a8620bd23846e1f98f7646cbd51dbc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(4x-3y)^4 = &amp; \\begin{pmatrix} 4 \\\\ 0 \\end{pmatrix} (4x)^4 \\cdot (3y)^0-\\begin{pmatrix} 4 \\\\ 1 \\end{pmatrix} (4x)^3 \\cdot (3y)^1+\\begin{pmatrix} 4 \\\\ 2 \\end{pmatrix} \\cdot (4x)^2 \\cdot (3y)^2 - \\\\[2ex] &amp; - \\begin{pmatrix} 4 \\\\ 3 \\end{pmatrix}(4x)^1 \\cdot (3y)^3+\\begin{pmatrix} 4 \\\\ 4 \\end{pmatrix}  (4x)^0 \\cdot (3y)^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"560\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u0627 \u0623\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0631\u0627\u0628\u0639\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 4 \u0645\u0646 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 \u0644\u0644\u0639\u062b\u0648\u0631 \u0645\u0628\u0627\u0634\u0631\u0629 \u0639\u0644\u0649 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062a\u0648\u0627\u0641\u0642\u064a\u0629: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/tirangulo-de-tartaglia-o-pascal-niveau-4.png\" alt=\"\u0647\u0631\u0645 \u0646\u064a\u0648\u062a\u0646 \u0630\u0648 \u0627\u0644\u062d\u062f\u064a\u0646\" class=\"wp-image-2100\" width=\"296\" height=\"232\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-128e8baa45ddd7d74703c9dfd4a19b06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(4x-3y)^4= &amp; \\ 1\\cdot  (4x)^4 \\cdot (3y)^0-4\\cdot  (4x)^3 \\cdot (3y)^1+6 \\cdot (4x)^2 \\cdot (3y)^2 - \\\\[2ex] &amp; - 4 \\cdot (4x)^1 \\cdot (3y)^3+1 \\cdot (4x)^0 \\cdot (3y)^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"504\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062f\u0631\u0643 \u062c\u0645\u064a\u0639 \u0627\u0644\u0635\u0644\u0627\u062d\u064a\u0627\u062a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f41577a79066a849e23154b5f55ac638_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot  256x^4 \\cdot 1-4\\cdot  64x^3 \\cdot 3y+6 \\cdot 16x^2 \\cdot 9y^2 - 4 \\cdot 4x \\cdot 27y^3+1 \\cdot 1 \\cdot 81y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"523\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0646\u062d\u0644 \u0627\u0644\u0636\u0631\u0628: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7790f8c6efcfc885ef79fcecdf89f2af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"256x^4-256x^3 \\cdot 3y+96x^2 \\cdot 9y^2 - 16x \\cdot 27y^3+81y^4\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"390\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c9e770e98c445da768bb1371975d48e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{256x^4-768x^3y+864x^2y^2-432xy^3+81y^4}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"334\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 5<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u062f\u062f \u0627\u0644\u062d\u062f \u0627\u0644\u0633\u0627\u0628\u0639 \u0641\u064a \u0645\u0641\u0643\u0648\u0643 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c76089bd0d5d4f499a0101d91669d461_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2x-5y)^{10}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"86\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0645\u0627 \u0623\u0646\u0647\u0627 \u0630\u0627\u062a \u062d\u062f\u064a\u0646 \u0633\u0627\u0644\u0628\u0629\u060c \u064a\u062c\u0628 \u0639\u0644\u064a\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f27311f76b6e99443d595efdc42e2286_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_k = (-1)^{k-1} \\begin{pmatrix} n \\\\ k-1 \\end{pmatrix} a^{n-k+1} b^{k-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"263\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0631\u064a\u062f \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u062d\u062f 7 \u0648\u064a\u062a\u0645 \u0631\u0641\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0642\u0648\u0629 10\u060c \u0644\u0630\u0644\u0643 \u0628\u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0642\u064a\u0645 \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629 \u064a\u0635\u0628\u062d:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65c821f4542af0fe95536ee191c7d430_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T_7= (-1)^{7-1} \\begin{pmatrix} 10 \\\\ 7-1 \\end{pmatrix} (2x)^{10-7+1} \\cdot (5y)^{7-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"326\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0630\u0644\u0643 \u064a\u0643\u0641\u064a \u0644\u0644\u0639\u0645\u0644 \u0623\u0646 \u0646\u0639\u0631\u0641 \u0645\u0635\u0637\u0644\u062d: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ded0622cbba2bff0563c2f9982c05142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} T_7 &amp; = (-1)^{6} \\begin{pmatrix} 10 \\\\ 6 \\end{pmatrix} (2x)^{4} \\cdot (5y)^{6} \\\\[2ex] &amp; = 1 \\cdot 210\\cdot  16x^4 \\cdot 15625y^6 \\\\[2ex] &amp; = \\bm{52500000x^4y^6} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"228\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Historia-del-Binomio-de-Newton\"><\/span> \u062a\u0627\u0631\u064a\u062e \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0623\u0635\u0644 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u064a\u0646\u0633\u0628 \u0625\u0644\u0649 \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u0625\u0646\u062c\u0644\u064a\u0632\u064a \u0627\u0644\u0634\u0647\u064a\u0631 \u0625\u0633\u062d\u0627\u0642 \u0646\u064a\u0648\u062a\u0646 (1642-1727)\u060c \u0625\u0644\u0627 \u0623\u0646\u0647 \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639 \u062a\u0645 \u0627\u0643\u062a\u0634\u0627\u0641 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0644\u0644\u0646\u0638\u0631\u064a\u0629 \u0644\u0623\u0648\u0644 \u0645\u0631\u0629 \u0639\u0644\u0649 \u064a\u062f \u0627\u0644\u0645\u0647\u0646\u062f\u0633 \u0627\u0644\u0641\u0627\u0631\u0633\u064a \u0627\u0644\u0643\u0627\u0631\u064a\u062c\u064a \u062d\u0648\u0627\u0644\u064a \u0639\u0627\u0645 1000\u060c \u0628\u0644 \u0648\u0642\u062f \u062a\u0645 \u0627\u0643\u062a\u0634\u0627\u0641 \u0630\u0644\u0643 \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0639\u0634\u0631\u060c \u0643\u0627\u0646 \u0639\u0644\u0645\u0627\u0621 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0635\u064a\u0646\u064a\u0648\u0646 \u064a\u0627\u0646\u063a \u0647\u0648\u064a \u0648\u062a\u0634\u0648\u0647 \u0634\u064a\u0647 \u062a\u0634\u064a\u0647 \u064a\u0639\u0631\u0641\u0648\u0646 \u0628\u0627\u0644\u0641\u0639\u0644 \u0627\u0644\u062a\u0648\u0633\u0639\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0644\u062f\u0631\u062c\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0627\u062d\u0642\u064b\u0627\u060c \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u0633\u0627\u0628\u0639 \u0639\u0634\u0631\u060c \u0628\u0646\u0649 \u0646\u064a\u0648\u062a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0623\u0633\u0633 \u0627\u0644\u062a\u064a \u0648\u0636\u0639\u0647\u0627 \u0639\u0644\u0645\u0627\u0621 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0648\u0646 \u0644\u062a\u0648\u0633\u064a\u0639 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646. \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0623\u0633\u0627\u0644\u064a\u0628 \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u062c\u0648\u0646 \u0648\u0648\u0644\u0632 \u0641\u064a \u0627\u0644\u0627\u0633\u062a\u064a\u0641\u0627\u0621 \u0648\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0621 \u0648\u0645\u0641\u0627\u0647\u064a\u0645 \u0627\u0644\u0623\u0633\u0633 \u0627\u0644\u0645\u0639\u0645\u0645\u0629\u060c \u0643\u0627\u0646 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649 \u062a\u062d\u0648\u064a\u0644 \u062a\u0639\u0628\u064a\u0631 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f \u0625\u0644\u0649 \u0633\u0644\u0633\u0644\u0629 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0648\u0627\u0644\u064a \u0639\u0627\u0645 1665\u060c \u0646\u062c\u062d \u0646\u064a\u0648\u062a\u0646 \u0641\u064a \u0625\u062b\u0628\u0627\u062a \u0623\u0646 \u0627\u0644\u0623\u0633 n \u0644\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0623\u0633\u064b\u0627 \u0639\u0642\u0644\u0627\u0646\u064a\u064b\u0627\u060c \u0648\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u062d\u0644 \u0642\u0648\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0623\u0633 \u0643\u0633\u0631\u064b\u0627. \u0648\u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0641\u0642\u062f \u062b\u0628\u062a \u0630\u0644\u0643 \u0623\u064a\u0636\u064b\u0627 \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633 \u0627\u0644\u0633\u0627\u0644\u0628. \u0648\u0627\u0644\u0645\u0641\u0627\u062c\u0623\u0629 \u0623\u0646\u0647 \u0627\u0643\u062a\u0634\u0641 \u0623\u0646 \u062a\u0637\u0648\u0631\u0627\u062a \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u064a\u0646 \u0647\u064a \u0633\u0644\u0633\u0644\u0629 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0639 \u0647\u0630\u0627 \u0627\u0644\u0627\u0643\u062a\u0634\u0627\u0641\u060c \u0628\u062f\u0623 \u0646\u064a\u0648\u062a\u0646 \u0641\u064a \u0627\u0644\u062a\u0634\u0643\u064a\u0643 \u0641\u064a \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u0633\u0644\u0633\u0644\u0629 \u0627\u0644\u0644\u0627\u0646\u0647\u0627\u0626\u064a\u0629 \u0648\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629\u060c \u0648\u0627\u0633\u062a\u0646\u062a\u062c \u0623\u0646\u0647 \u064a\u0645\u0643\u0646 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0645\u0639 \u0633\u0644\u0633\u0644\u0629 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u0629 \u0628\u0646\u0641\u0633 \u0637\u0631\u064a\u0642\u0629 \u062a\u0639\u0628\u064a\u0631\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062d\u062f\u0648\u062f\u0629. \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0646\u064a\u0648\u062a\u0646 \u0644\u0645 \u064a\u0646\u0634\u0631 \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0645\u0637\u0644\u0642\u064b\u0627\u060c \u0625\u0644\u0627 \u0623\u0646 \u062c\u0648\u0646 \u0648\u0648\u0644\u0632 \u0641\u0639\u0644 \u0630\u0644\u0643 \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0641\u064a \u0639\u0627\u0645 1685\u060c \u0648\u0646\u0633\u0628 \u0627\u0644\u0641\u0636\u0644 \u0625\u0644\u0649 \u0646\u064a\u0648\u062a\u0646 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0627\u0643\u062a\u0634\u0627\u0641.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\" style=\";text-align:right;direction:rtl\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0634\u0631\u062d\u0627 \u0644\u0645\u0627\u0647\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646 \u0648\u0645\u0627 \u0647\u064a \u0635\u064a\u063a\u062a\u0647\u0627. \u064a\u0645\u0643\u0646\u0643 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646 \u062a\u0631\u0649 \u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637 \u0630\u0644\u0643 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644). \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062c\u062f \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0628\u0634\u0623\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 \u0648\u062c\u0645\u064a\u0639 \u062e\u0635\u0627\u0626\u0635\u0647\u0627. \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0633\u0646\u0634\u0631\u062d \u0627\u0644\u0641\u0636\u0648\u0644 \u0648\u0631\u0627\u0621 \u0623\u0635\u0644 \u0647\u0630\u0647 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u062c\u062f\u064b\u0627. \u0645\u0627 \u0647\u064a \u0630\u0627\u062a &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/\"> <span class=\"screen-reader-text\">\u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)<\/span> \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0645\u0632\u064a\u062f &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[2],"tags":[],"class_list":["post-67","post","type-post","status-publish","format-standard","hentry","category-2"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)<\/title>\n<meta name=\"description\" content=\"\u0634\u0631\u062d \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646: \u0645\u0627 \u0647\u064a\u060c \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062a\u0628\u0633\u064a\u0637\u0647\u0627 \u0628\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644)\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c \u062a\u0627\u0631\u064a\u062e\u060c.. .\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ar\/\u0635\u064a\u063a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0623\u0648-\u0646\u0638\u0631\u064a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0644\u0646\u064a\/\" \/>\n<meta property=\"og:locale\" content=\"ar_AR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)\" \/>\n<meta property=\"og:description\" content=\"\u0634\u0631\u062d \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646: \u0645\u0627 \u0647\u064a\u060c \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062a\u0628\u0633\u064a\u0637\u0647\u0627 \u0628\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644)\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c \u062a\u0627\u0631\u064a\u062e\u060c.. .\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ar\/\u0635\u064a\u063a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0623\u0648-\u0646\u0638\u0631\u064a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0644\u0646\u064a\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-17T07:20:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8087bb711e716aca4a2c535eaeb8b0bf_l3.png\" \/>\n<meta name=\"author\" content=\"\u0641\u0631\u064a\u0642 Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0643\u064f\u062a\u0628 \u0628\u0648\u0627\u0633\u0637\u0629\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u0641\u0631\u064a\u0642 Mathority\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/\"},\"author\":{\"name\":\"\u0641\u0631\u064a\u0642 Mathority\",\"@id\":\"https:\/\/mathority.org\/ar\/#\/schema\/person\/b6c8cd3c82fb4228ce41b667b17bd613\"},\"headline\":\"\u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)\",\"datePublished\":\"2023-09-17T07:20:31+00:00\",\"dateModified\":\"2023-09-17T07:20:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/\"},\"wordCount\":11,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/ar\/#organization\"},\"articleSection\":[\"\u0630\u0648\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646\"],\"inLanguage\":\"ar\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/\",\"url\":\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/\",\"name\":\"\u25b7 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/ar\/#website\"},\"datePublished\":\"2023-09-17T07:20:31+00:00\",\"dateModified\":\"2023-09-17T07:20:31+00:00\",\"description\":\"\u0634\u0631\u062d \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646: \u0645\u0627 \u0647\u064a\u060c \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062a\u0628\u0633\u064a\u0637\u0647\u0627 \u0628\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644)\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c \u062a\u0627\u0631\u064a\u062e\u060c.. .\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#breadcrumb\"},\"inLanguage\":\"ar\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/ar\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/ar\/#website\",\"url\":\"https:\/\/mathority.org\/ar\/\",\"name\":\"Mathority\",\"description\":\"\u062d\u064a\u062b \u064a\u0644\u062a\u0642\u064a \u0627\u0644\u0641\u0636\u0648\u0644 \u0628\u0627\u0644\u062d\u0633\u0627\u0628!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/ar\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/ar\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"ar\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/ar\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/ar\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ar\",\"@id\":\"https:\/\/mathority.org\/ar\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/ar\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/ar\/wp-content\/uploads\/2023\/10\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/ar\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/ar\/#\/schema\/person\/b6c8cd3c82fb4228ce41b667b17bd613\",\"name\":\"\u0641\u0631\u064a\u0642 Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"ar\",\"@id\":\"https:\/\/mathority.org\/ar\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g\",\"caption\":\"\u0641\u0631\u064a\u0642 Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/ar\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u25b7 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)","description":"\u0634\u0631\u062d \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646: \u0645\u0627 \u0647\u064a\u060c \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062a\u0628\u0633\u064a\u0637\u0647\u0627 \u0628\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644)\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c \u062a\u0627\u0631\u064a\u062e\u060c.. .","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/ar\/\u0635\u064a\u063a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0623\u0648-\u0646\u0638\u0631\u064a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0644\u0646\u064a\/","og_locale":"ar_AR","og_type":"article","og_title":"\u25b7 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)","og_description":"\u0634\u0631\u062d \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646: \u0645\u0627 \u0647\u064a\u060c \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062a\u0628\u0633\u064a\u0637\u0647\u0627 \u0628\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644)\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c \u062a\u0627\u0631\u064a\u062e\u060c.. .","og_url":"https:\/\/mathority.org\/ar\/\u0635\u064a\u063a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0623\u0648-\u0646\u0638\u0631\u064a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0644\u0646\u064a\/","article_published_time":"2023-09-17T07:20:31+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8087bb711e716aca4a2c535eaeb8b0bf_l3.png"}],"author":"\u0641\u0631\u064a\u0642 Mathority","twitter_card":"summary_large_image","twitter_misc":{"\u0643\u064f\u062a\u0628 \u0628\u0648\u0627\u0633\u0637\u0629":"\u0641\u0631\u064a\u0642 Mathority"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/"},"author":{"name":"\u0641\u0631\u064a\u0642 Mathority","@id":"https:\/\/mathority.org\/ar\/#\/schema\/person\/b6c8cd3c82fb4228ce41b667b17bd613"},"headline":"\u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)","datePublished":"2023-09-17T07:20:31+00:00","dateModified":"2023-09-17T07:20:31+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/"},"wordCount":11,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/ar\/#organization"},"articleSection":["\u0630\u0648\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646"],"inLanguage":"ar","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/","url":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/","name":"\u25b7 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)","isPartOf":{"@id":"https:\/\/mathority.org\/ar\/#website"},"datePublished":"2023-09-17T07:20:31+00:00","dateModified":"2023-09-17T07:20:31+00:00","description":"\u0634\u0631\u062d \u0643\u0644 \u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0623\u0648 \u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646) \u0644\u0646\u064a\u0648\u062a\u0646: \u0645\u0627 \u0647\u064a\u060c \u0635\u064a\u063a\u062a\u0647\u0627\u060c \u0643\u064a\u0641\u064a\u0629 \u062a\u0628\u0633\u064a\u0637\u0647\u0627 \u0628\u0645\u062b\u0644\u062b \u062a\u0627\u0631\u062a\u0627\u0644\u064a\u0627 (\u0623\u0648 \u0628\u0627\u0633\u0643\u0627\u0644)\u060c \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629\u060c \u062e\u0635\u0627\u0626\u0635\u060c \u062a\u0627\u0631\u064a\u062e\u060c.. .","breadcrumb":{"@id":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#breadcrumb"},"inLanguage":"ar","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/ar\/%d8%b5%d9%8a%d8%ba%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d8%a3%d9%88-%d9%86%d8%b8%d8%b1%d9%8a%d8%a9-%d8%b0%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86-%d9%84%d9%86%d9%8a\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/ar\/"},{"@type":"ListItem","position":2,"name":"\u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0646\u0638\u0631\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646)"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/ar\/#website","url":"https:\/\/mathority.org\/ar\/","name":"Mathority","description":"\u062d\u064a\u062b \u064a\u0644\u062a\u0642\u064a \u0627\u0644\u0641\u0636\u0648\u0644 \u0628\u0627\u0644\u062d\u0633\u0627\u0628!","publisher":{"@id":"https:\/\/mathority.org\/ar\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/ar\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"ar"},{"@type":"Organization","@id":"https:\/\/mathority.org\/ar\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/ar\/","logo":{"@type":"ImageObject","inLanguage":"ar","@id":"https:\/\/mathority.org\/ar\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/ar\/wp-content\/uploads\/2023\/10\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/ar\/wp-content\/uploads\/2023\/10\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/ar\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/ar\/#\/schema\/person\/b6c8cd3c82fb4228ce41b667b17bd613","name":"\u0641\u0631\u064a\u0642 Mathority","image":{"@type":"ImageObject","inLanguage":"ar","@id":"https:\/\/mathority.org\/ar\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/dd3f98feaeb54f342e72193f2059ae90dc3178f59adb7c82b33fc7d71c6ee19d?s=96&d=mm&r=g","caption":"\u0641\u0631\u064a\u0642 Mathority"},"sameAs":["http:\/\/mathority.org\/ar"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/posts\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/comments?post=67"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/posts\/67\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/media?parent=67"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/categories?post=67"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/ar\/wp-json\/wp\/v2\/tags?post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}