{"id":344,"date":"2023-07-06T03:44:20","date_gmt":"2023-07-06T03:44:20","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d8%b1%d8%a8%d8%b9-%d8%b0%d9%88-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86\/"},"modified":"2023-07-06T03:44:20","modified_gmt":"2023-07-06T03:44:20","slug":"%d8%b1%d8%a8%d8%b9-%d8%b0%d9%88-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d8%b1%d8%a8%d8%b9-%d8%b0%d9%88-%d8%a7%d9%84%d8%ad%d8%af%d9%8a%d9%86\/","title":{"rendered":"\u0632\u0648\u062c \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0639"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0635\u064a\u063a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0644\u0631\u0627\u0628\u0639\u060c \u0648\u0646\u0634\u0631\u062d \u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0639 \u0627\u0644\u0623\u0645\u062b\u0644\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \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 \u0645\u0646 \u0623\u0642\u0631\u0627\u0646\u0643 \u0625\u0644\u0649 \u0627\u0644\u0635\u0641 \u0627\u0644\u0631\u0627\u0628\u0639. <\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Formula-del-binomio-a-la-cuarta\"><\/span> \u0635\u064a\u063a\u0629 \u0627\u0644\u0631\u0628\u0639 \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\"> \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c <strong>\u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0644\u0642\u0648\u0629 \u0623\u0631\u0628\u0639\u0629<\/strong> \u0647\u064a \u0643\u062b\u064a\u0631\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0644\u062d\u0633\u0627\u0628 \u0631\u0628\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \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-72f362dcdac7a948e05876758e78e7c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0645\u0646 <a href=\"https:\/\/mathority.org\/ar\/\u0635\u064a\u063a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0627\u0654\u0648-\u0646\u0638\u0631\u064a\u0629-\u0630\u0627\u062a-\u0627\u0644\u062d\u062f\u064a\u0646-\u0644\u0646\u064a\u0648\u062a\u0646-\u0648\u062a\u0645\u0627\u0631\u064a\u0646-\u0645\u062d\u0644\u0648\u0644\u0629\/\"><strong><span style=\"text-decoration: underline;\">\u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0627\u0644\u0639\u0627\u0645\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<\/span><\/strong><\/a> . \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u064a\u0645\u0643\u0646\u0643 \u062d\u0633\u0627\u0628 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0623\u064a \u0642\u0648\u0629\u060c \u0644\u0630\u0644\u0643 \u0645\u0646 \u0627\u0644\u0623\u0641\u0636\u0644 \u0623\u0646 \u062a\u062a\u0639\u0644\u0645 \u0635\u064a\u063a\u0629 \u0646\u064a\u0648\u062a\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646. \u0627\u0646\u0642\u0631 \u0639\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0637 \u0627\u0644\u0633\u0627\u0628\u0642 \u0648\u0627\u0643\u062a\u0634\u0641 \u0643\u064a\u0641 \u062a\u0628\u062f\u0648 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0641\u0625\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0639 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 \u0645\u0631\u0641\u0648\u0639\u064b\u0627 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 4 \u0641\u064a \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 \u062a\u0643\u0639\u064a\u0628 \u0648\u0627\u0644\u062d\u062f \u0627\u0644\u062b\u0627\u0646\u064a\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u0623\u0648\u0644 \u0648\u0627\u0644\u062b\u0627\u0646\u064a \u062a\u0631\u0628\u064a\u0639 \u0641\u064a 6\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 4 \u0641\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 \u0645\u0636\u0631\u0648\u0628\u064b\u0627 \u0641\u064a \u0627\u0644\u062d\u062f \u0627\u0644\u062b\u0627\u0646\u064a \u0645\u0631\u0641\u0648\u0639\u064b\u0627 \u0625\u0644\u0649 3\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u062d\u062f \u0627\u0644\u062b\u0627\u0646\u064a \u0645\u0631\u0641\u0648\u0639\u064b\u0627 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062a\u0648\u0627\u0641\u0642 \u0647\u0630\u0647 \u0627\u0644\u0635\u064a\u063a\u0629 \u0645\u0639 \u0645\u062c\u0645\u0648\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 (\u0639\u0646\u0635\u0631\u064a\u0647\u0627 \u0645\u0648\u062c\u0628\u0627\u0646)\u060c \u0644\u0643\u0646 \u0641\u064a <strong>\u0635\u064a\u063a\u0629 \u0627\u0644\u0637\u0631\u062d \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646<\/strong> \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639\u060c \u062a\u0643\u0648\u0646 \u0639\u0644\u0627\u0645\u0627\u062a \u0627\u0644\u0646\u0627\u062a\u062c\u064a\u0646 \u0627\u0644\u062b\u0627\u0646\u064a \u0648\u0627\u0644\u0631\u0627\u0628\u0639 \u0633\u0627\u0644\u0628\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-ab80a7a5a90fe6612c4474b5d7a8ae6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a \\color{red}\\bm{-}\\color{black}b)^4 = a^4\\color{red}\\bm{-}\\color{black}4a^3b+6a^2b^2\\color{red}\\bm{-}\\color{black}4ab^3+b^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"484\" 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=\"Ejemplos-de-binomios-a-la-cuarta\"><\/span> \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0623\u0642\u0631\u0627\u0646\u0647\u0645 \u0641\u064a \u0627\u0644\u0635\u0641 \u0627\u0644\u0631\u0627\u0628\u0639<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646\u060c \u0633\u0646\u0631\u0649 \u0639\u062f\u0629 \u0623\u0645\u062b\u0644\u0629 \u0644\u062d\u0644 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639. \u0633\u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627 \u0628\u062d\u0633\u0627\u0628 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u0645\u0648\u062c\u0628 \u062b\u0645 \u0633\u0646\u0642\u0648\u0645 \u0628\u062d\u0644 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u0633\u0627\u0644\u0628\u0629.<\/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\"> \u0627\u062d\u0633\u0628 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639:<\/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-03f5e137fa0eccec573bc15307d33cd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+2)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0635\u064a\u063a\u0629 \u0642\u0648\u0629 \u0645\u062c\u0645\u0648\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u064b\u0627 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639 \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-72f362dcdac7a948e05876758e78e7c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0627 \u0644\u062d\u0633\u0627\u0628 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u062a\u0645\u0631\u064a\u0646\u060c \u0645\u0627 \u0639\u0644\u064a\u0643 \u0633\u0648\u0649 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0645\u0642\u062f\u0627\u0631\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \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-1517da3b83cb1367db7ebf73c8600ce5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+2)^4 = x^4+4\\cdot x^3\\cdot 2+6\\cdot x^2\\cdot 2^2+4\\cdot x\\cdot 2^3+2^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"396\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627 \u0646\u062d\u0644 \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-4e84ddbeb643abf6cdce05666af6d41c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x+2)^4 &amp; = x^4+4\\cdot x^3\\cdot 2+6\\cdot x^2\\cdot 4+4\\cdot x\\cdot 8+16 \\\\[2ex] &amp; =x^4+8 x^3+24x^2+32x+16\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"383\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 2<\/h3>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639:<\/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-210f9597e603db7f4e3c41d2d5a1cd9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-3)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0642\u0648\u064a\u0629 \u0644\u0641\u0631\u0642 \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u064b\u0627 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639 \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-d5774034dc5f470b13498faa68571db6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^4 = a^4-4a^3b+6a^2b^2-4ab^3+b^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"310\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0630\u0644\u0643\u060c \u0644\u062a\u062d\u062f\u064a\u062f \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0644\u0645\u0634\u0643\u0644\u0629\u060c \u0645\u0627 \u0639\u0644\u064a\u0643 \u0633\u0648\u0649 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0641\u064a \u0627\u0644\u0635\u064a\u063a\u0629 \u0628\u0642\u064a\u0645 \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-116893deddf1913174508c08c874b685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x-3)^4 = x^4-4\\cdot x^3\\cdot 3+6\\cdot x^2\\cdot 3^2-4\\cdot x\\cdot 3^3+3^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"396\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627\u060c \u0646\u0642\u0648\u0645 \u0628\u062d\u0644 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0646\u0627\u062a\u062c\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-aa9fd790c949488c4124c2370fff7ea4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x-3)^4 &amp; = x^4-4\\cdot x^3\\cdot 3+6\\cdot x^2\\cdot 9-4\\cdot x\\cdot 27+81 \\\\[2ex] &amp; =x^4-12x^3+54x^2-108x+81\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"391\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-de-un-binomio-a-la-cuarta\"><\/span> \u0628\u064a\u0627\u0646 \u0635\u064a\u063a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0631\u0627\u0628\u0639<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0644\u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0645\u0641\u0647\u0648\u0645 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639\u060c \u0633\u0648\u0641 \u0646\u0628\u064a\u0646 \u0635\u064a\u063a\u062a\u0647\u0627 \u0628\u0639\u062f\u0629 \u0637\u0631\u0642.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0623\u064a \u0632\u0648\u062c \u0645\u0631\u0641\u0648\u0639 \u0625\u0644\u0649 4:<\/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-221292a85028b8f8aeec1e8878d7e4d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u0645\u0643\u0646 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062c\u0628\u0631\u064a \u0630\u064a \u0627\u0644\u062d\u062f\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\u0639 \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u0648\u0633\u064a\u0639\u0647 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644 \u0623\u0648\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-cb4cda88fca732a0609abddf72c7d2ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^4=(a+b)\\cdot (a+b)\\cdot (a+b)\\cdot (a+b)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"330\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0647\u0643\u0630\u0627\u060c \u0645\u0646 \u062e\u0644\u0627\u0644 \u062d\u0644 \u0643\u0644 <a href=\"https:\/\/mathority.org\/ar\/\u0636\u0631\u0628-\u0643\u062b\u064a\u0631\u0627\u062a-\u0627\u0644\u062d\u062f\u0648\u062f\u060c-\u0627\u0654\u0645\u062b\u0644\u0629\u060c-\u062a\u0645\u0627\u0631\u064a\u0646-\u062d\u0644-\u0636\u0631\u0628-\u0627\u0644\u0645\u0646\u062a\u062c\/\"><strong><span style=\"text-decoration: underline;\">\u0645\u0646\u062a\u062c \u0645\u0646 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f<\/span><\/strong><\/a> \u060c \u0646\u0635\u0644 \u0625\u0644\u0649 \u0635\u064a\u063a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\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-1f1fccc8f73eedbccfa9ef436549c932_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (a+b)^4 &amp; =(a+b)\\cdot (a+b)\\cdot (a+b)\\cdot (a+b) \\\\[2ex] &amp;= (a^2+2ab+b^2)\\cdot (a+b)\\cdot (a+b) \\\\[2ex] &amp; = (a^3+3a^2b+3ab^2+b^3) \\cdot (a+b) \\\\[2ex] &amp; = a^4+4a^3b+6a^2b^2+4ab^3+b^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"150\" width=\"330\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0635\u064a\u063a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0644\u0623\u0631\u0628\u0639\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 <a href=\"https:\/\/mathority.org\/ar\/\u0645\u0643\u0639\u0628-\u0630\u0648-\u0627\u0644\u062d\u062f\u064a\u0646\/\"><strong><span style=\"text-decoration: underline;\">\u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0645\u0643\u0639\u0628<\/span><\/strong><\/a> :<\/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-b87645d508e38be4981e6cd954490f72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (a+b)^4 &amp; =(a+b)^3 \\cdot (a+b)\\\\[2ex] &amp; = (a^3+3a^2b+3ab^2+b^3) \\cdot (a+b) \\\\[2ex] &amp; = a^4+4a^3b+6a^2b^2+4ab^3+b^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"326\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0645\u0646\u062a\u062c\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0632\u0629 (\u0623\u0648 \u0627\u0644\u0647\u0648\u064a\u0627\u062a \u0627\u0644\u0628\u0627\u0631\u0632\u0629). \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/ar\/\u0645\u0631\u0628\u0639-\u0645\u062c\u0645\u0648\u0639-\u0627\u0654\u0648-\u0645\u062c\u0645\u0648\u0639-\u0645\u0631\u0628\u0639\/\">\u0627\u0644\u0645\u0646\u062a\u062c \u0627\u0644\u0628\u0627\u0631\u0632 \u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0645\u062c\u0645\u0648\u0639<\/a><\/span><\/strong> :<\/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-f6a8ef4bfb728886326da5d4fd39974a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (a+b)^4 &amp; =(a+b)^2\\cdot (a+b)^2 \\\\[2ex] &amp;= (a^2+2ab+b^2)\\cdot (a^2+2ab+b^2) \\\\[2ex]  &amp; = a^4+4a^3b+6a^2b^2+4ab^3+b^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"325\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a\u060c \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0635\u064a\u063a\u0629 \u0627\u0644\u0647\u0648\u064a\u0629 \u0627\u0644\u0628\u0627\u0631\u0632\u0629 <a href=\"https:\/\/mathority.org\/ar\/\u0645\u0631\u0628\u0639-\u0627\u0644\u0641\u0631\u0642-\u0627\u0654\u0648-\u0627\u0644\u0637\u0631\u062d\/\"><strong><span style=\"text-decoration: underline;\">\u0644\u0645\u0631\u0628\u0639 \u0627\u0644\u0637\u0631\u062d<\/span><\/strong><\/a> \u0644\u062a\u0623\u0643\u064a\u062f \u0635\u064a\u063a\u0629 \u0627\u0644\u0637\u0631\u062d \u0630\u064a \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-14234e8714d33a06a9c2b029fec252d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (a-b)^4 &amp; =(a-b)^2\\cdot (a-b)^2 \\\\[2ex] &amp;= (a^2-2ab+b^2)\\cdot (a^2-2ab+b^2) \\\\[2ex]  &amp; = a^4-4a^3b+6a^2b^2-4ab^3+b^4 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"325\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-binomios-a-la-cuarta\"><\/span> \u062a\u0645\u0627\u0631\u064a\u0646 \u0645\u062d\u0644\u0648\u0644\u0629 \u0644\u0644\u0623\u0632\u0648\u0627\u062c \u0641\u064a \u0627\u0644\u0635\u0641 \u0627\u0644\u0631\u0627\u0628\u0639<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0627\u0644\u0642\u0648\u0649 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0646 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u0629 \u0625\u0644\u0649 \u0627\u0644\u0631\u0627\u0628\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-78de0250a24376eafa33b75828530e55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x+1)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"88\" 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-c55ffad970f894d6ceb6951057bfe5aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ (2x+3)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"96\" 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-fdd88fec0f06da304ff2999b733fc313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ (x-4)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"87\" 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-33170b079c2a7a10373f56099500b550_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ (x^2+y)^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"96\" 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 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-063eb752a20c15adfc0eec5a42b9d67e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned} (x+1)^4 &amp; = x^4 +4\\cdot x^3\\cdot 1+6 \\cdot x^2\\cdot 1^2+4 \\cdot x\\cdot 1^3 + 1^4 \\\\[2ex]  &amp; = x^4 +4\\cdot x^3\\cdot 1+6 \\cdot x^2\\cdot 1+4 \\cdot x\\cdot 1 + 1 \\\\[2ex]  &amp; = \\bm{x^4 +4x^3+6 x^2+4 x + 1}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"429\" style=\"vertical-align: 0px;\"><\/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-707c85ccb35055d4fece1d058b46217a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned} (2x+3)^4 &amp; = (2x)^4 +4\\cdot (2x)^3\\cdot 3+6 \\cdot (2x)^2\\cdot 3^2+4 \\cdot 2x\\cdot 3^3 + 3^4 \\\\[2ex]  &amp; = 16x^4 +4\\cdot 8x^3\\cdot 3+6 \\cdot 4x^2\\cdot 9+4 \\cdot 2x\\cdot 27 + 81\\\\[2ex]  &amp; = \\bm{16x^4 +96x^3+216x^2+216x + 81}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"514\" style=\"vertical-align: 0px;\"><\/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-ce610d6757b7ce6fb5dfaa3b0679f368_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{aligned} (x-4)^4 &amp; = x^4 -4\\cdot x^3\\cdot 4+6 \\cdot x^2\\cdot 4^2-4 \\cdot x\\cdot 4^3 + 4^4 \\\\[2ex]  &amp; = x^4 -4\\cdot x^3\\cdot 4+6 \\cdot x^2\\cdot 16-4 \\cdot x\\cdot 64 + 256 \\\\[2ex] &amp; = \\bm{x^4 -16 x^3+96x^2-256x + 256}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"442\" style=\"vertical-align: 0px;\"><\/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-4f5ca1d6b47e6ed78f64deff8122ed3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{aligned} (x^2+y)^4 &amp; = \\left(x^2\\right)^4 +4\\cdot \\left(x^2\\right)^3\\cdot y+6 \\cdot \\left(x^2\\right)^2\\cdot y^2+4 \\cdot x^2\\cdot y^3 + y^4 \\\\[2ex] &amp; =x^8 +4\\cdot x^6\\cdot y+6 \\cdot x^4\\cdot y^2+4 \\cdot x^2\\cdot y^3 + y^4 \\\\[2ex]  &amp; = \\bm{x^8 +4x^6y+6 x^4 y^2+4x^2y^3 + y^4}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"519\" 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<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 \u0635\u064a\u063a\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0644\u0631\u0627\u0628\u0639\u060c \u0648\u0646\u0634\u0631\u062d \u0643\u064a\u0641\u064a\u0629 \u062d\u0644 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0645\u0639 \u0627\u0644\u0623\u0645\u062b\u0644\u0629. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u0649 \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 \u0645\u0646 \u0623\u0642\u0631\u0627\u0646\u0643 \u0625\u0644\u0649 \u0627\u0644\u0635\u0641 \u0627\u0644\u0631\u0627\u0628\u0639. \u0635\u064a\u063a\u0629 \u0627\u0644\u0631\u0628\u0639 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0644\u0642\u0648\u0629 \u0623\u0631\u0628\u0639\u0629 \u0647\u064a \u0643\u062b\u064a\u0631\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u062d\u062f\u064a\u0646 \u0645\u0631\u0641\u0648\u0639\u064a\u0646 \u0625\u0644\u0649 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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