{"id":66,"date":"2023-09-17T07:20:31","date_gmt":"2023-09-17T07:20:31","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%82%d0%b5%d0%be%d1%80%d0%b5%d0%bc%d1%8b-%d0%b8%d0%bb%d0%b8-%d0%b1%d0%b8%d0%bd\/"},"modified":"2023-09-17T07:20:31","modified_gmt":"2023-09-17T07:20:31","slug":"%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%82%d0%b5%d0%be%d1%80%d0%b5%d0%bc%d1%8b-%d0%b8%d0%bb%d0%b8-%d0%b1%d0%b8%d0%bd","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%82%d0%b5%d0%be%d1%80%d0%b5%d0%bc%d1%8b-%d0%b8%d0%bb%d0%b8-%d0%b1%d0%b8%d0%bd\/","title":{"rendered":"\u0411\u0438\u043d\u043e\u043c \u043d\u044c\u044e\u0442\u043e\u043d\u0430 (\u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430)"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 (\u0438\u043b\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430) \u0438 \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u044d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 (\u0438\u043b\u0438 \u041f\u0430\u0441\u043a\u0430\u043b\u044f). \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0434\u043b\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0438 \u0432\u0441\u0435\u0445 \u0435\u0433\u043e \u0441\u0432\u043e\u0439\u0441\u0442\u0432. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \u043a\u0443\u0440\u044c\u0435\u0437\u044b, \u043b\u0435\u0436\u0430\u0449\u0438\u0435 \u0432 \u043e\u0441\u043d\u043e\u0432\u0435 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u043e\u0447\u0435\u043d\u044c \u043a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-binomio-de-Newton\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> \u0412 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 <strong>\u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430<\/strong> , \u0442\u0430\u043a\u0436\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0439 \u043a\u0430\u043a <strong>\u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043e \u0431\u0438\u043d\u043e\u043c\u0435<\/strong> , \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0443\u044e \u043b\u0435\u0433\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0431\u0438\u043d\u043e\u043c\u0430. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043c\u043e\u0436\u043d\u043e <sup>\u0440\u0435\u0448\u0438\u0442\u044c<\/sup> \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0432\u0438\u0434\u0430 (a+b).<\/p>\n<p> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u044d\u0442\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u043d\u0430\u0437\u0432\u0430\u043d\u0430 \u0432 \u0447\u0435\u0441\u0442\u044c \u0444\u0438\u0437\u0438\u043a\u0430, \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0444\u0438\u043b\u043e\u0441\u043e\u0444\u0430 \u0441\u044d\u0440\u0430 \u0418\u0441\u0430\u0430\u043a\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430. \u041e\u0434\u043d\u0430\u043a\u043e \u0432 \u044d\u0442\u043e\u043c \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0440\u0430\u0437\u043d\u043e\u0433\u043b\u0430\u0441\u0438\u044f, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0431\u044b\u043b\u0438 \u043d\u0430\u0439\u0434\u0435\u043d\u044b \u0431\u043b\u0438\u0436\u043d\u0435\u0432\u043e\u0441\u0442\u043e\u0447\u043d\u044b\u0435 \u0442\u0435\u043a\u0441\u0442\u044b, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u044d\u0442\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0443\u0436\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043b\u0430\u0441\u044c. \u041d\u0438\u0436\u0435 \u043c\u044b \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u043e\u0431\u0441\u0443\u0434\u0438\u043c \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u044d\u0442\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u044b. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-binomio-de-Newton\"><\/span>\u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u044d\u0442\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0431\u0438\u043d\u043e\u043c\u043e\u0432. \u041d\u043e\u2026 \u043a\u0430\u043a \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430? \u0418\u043b\u0438, \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430? <\/p>\n<div style=\"background-color:#ffebee;padding-top: 20px; padding-bottom: 0.5px; padding-right: 40px; padding-left: 30px; border-radius:20px;\">\n<p style=\"text-align:left\"> <strong>\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430<\/strong> \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<\/p>\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> \u0418\u043b\u0438 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442:<\/p>\n<\/p>\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> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u0436\u043d\u0430 \u0434\u043b\u044f \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044f \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043b\u0438 \u043d\u0438\u0436\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0431\u0438\u043d\u043e\u043c\u043e\u0432 \u043d\u0438\u0437\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0435\u0435 \u043b\u0443\u0447\u0448\u0435 \u043f\u043e\u043d\u044f\u0442\u044c: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u041d\u044c\u044e\u0442\u043e\u043d\u0430\" class=\"wp-image-2126\" width=\"578\" height=\"578\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u043f\u0440\u0438 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0438 \u0431\u0438\u043d\u043e\u043c\u0430 <strong>\u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0438 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e (\u0430) \u0443\u043c\u0435\u043d\u044c\u0448\u0430\u044e\u0442\u0441\u044f,<\/strong> \u0430 <strong>\u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0438 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e (\u0431) \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u044e\u0442\u0441\u044f<\/strong> , \u0442\u0430\u043a \u0436\u0435, \u043a\u0430\u043a \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043c\u043b\u0430\u0434\u0448\u0438\u0439 \u044d\u043b\u0435\u043c\u0435\u043d\u0442 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b.<\/p>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u0435\u043e\u0440\u0435\u043c\u0443, \u043d\u0443\u0436\u043d\u043e \u0443\u043c\u0435\u0442\u044c \u0440\u0435\u0448\u0430\u0442\u044c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0442\u043e \u0435\u0441\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432\u0438\u0434\u0430<\/p>\n<\/p>\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> . \u0418\u0442\u0430\u043a, \u043f\u0440\u0435\u0436\u0434\u0435 \u0447\u0435\u043c \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043a\u0440\u0430\u0442\u043a\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Numero-combinatorio\"><\/span> \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0414\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f <strong>\u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430<\/strong> (\u0438\u043b\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430) \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443:<\/p>\n<\/p>\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> \u0417\u043e\u043b\u043e\u0442\u043e<\/p>\n<\/p>\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> \u0418<\/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> \u042d\u0442\u043e <strong>\u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0430\u043b\u044b<\/strong> . \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0442\u0430\u043a\u0436\u0435 \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0444\u0430\u043a\u0442\u043e\u0440\u0438\u0430\u043b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0443\u0442\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0432\u0441\u0435\u0445 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b, \u0440\u0430\u0432\u043d\u044b\u0445 1, \u043d\u0430 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e:<\/p>\n<\/p>\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> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043c\u044b \u043d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f:<\/p>\n<\/p>\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> \u041a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u043c\u043e\u0436\u043d\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0438 \u0447\u0435\u0440\u0435\u0437 \u043a\u0430\u043b\u044c\u043a\u0443\u043b\u044f\u0442\u043e\u0440 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043a\u043b\u0430\u0432\u0438\u0448\u0438 <\/p>\n<\/p>\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\"><span class=\"ez-toc-section\" id=\"Ejemplos-del-binomio-de-Newton\"><\/span> \u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u041d\u044c\u044e\u0442\u043e\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u0437\u043d\u0430\u0435\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430, \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043d\u0430 \u0434\u0432\u0443\u0445 \u0447\u0438\u0441\u043b\u043e\u0432\u044b\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445.<\/p>\n<h3 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u0440 1<\/h3>\n<ul>\n<li> \u041f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u0435 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u0447\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0430:<\/li>\n<\/ul>\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> \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e\u0442 \u0431\u0438\u043d\u043e\u043c \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442, \u0435\u0433\u043e \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u043e\u0440\u043c\u0443\u043b \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432 ( <strong><span style=\"text-decoration: underline;\"> \u043a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0430 <\/span><\/strong> ), \u043d\u043e \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0435\u0433\u043e \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b.<\/p>\n<p> \u041f\u0440\u0435\u0436\u0434\u0435 \u0432\u0441\u0435\u0433\u043e, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u041d\u044c\u044e\u0442\u043e\u043d\u0430:<\/p>\n<\/p>\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> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 n=2, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e:<\/p>\n<\/p>\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> \u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u0432\u043d\u0438\u043c\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u043d\u0430\u0447\u0430\u043b\u0435 \u043c\u044b \u043f\u043e\u0434\u043d\u0438\u043c\u0430\u0435\u043c \u043f\u0435\u0440\u0432\u043e\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 (x) \u0434\u043e \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0433\u043e, \u0447\u0442\u043e \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0440\u0430\u0432\u043d\u043e 2. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043c\u044b \u043f\u043e\u0434\u043d\u0438\u043c\u0430\u0435\u043c \u0432\u0442\u043e\u0440\u043e\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 (3) \u0434\u043e \u043c\u0438\u043d\u0438\u043c\u0430\u043b\u044c\u043d\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0433\u043e, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u0440\u0430\u0432\u043d\u043e 0. \u041d\u043e \u043f\u043e \u043c\u0435\u0440\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043c\u044b \u0434\u0432\u0438\u0436\u0435\u043c\u0441\u044f \u0432\u043f\u0440\u0430\u0432\u043e, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0442\u044c <strong>\u043f\u0435\u0440\u0432\u044b\u0439 \u0447\u043b\u0435\u043d \u0434\u043e \u043c\u0435\u043d\u044c\u0448\u0435\u0433\u043e \u0447\u0438\u0441\u043b\u0430, \u0447\u0435\u043c \u0440\u0430\u043d\u044c\u0448\u0435,<\/strong> \u0430 <strong>\u0432\u0442\u043e\u0440\u043e\u0439 \u0447\u043b\u0435\u043d \u0434\u043e \u0431\u043e\u043b\u044c\u0448\u0435\u0433\u043e \u0447\u0438\u0441\u043b\u0430, \u0447\u0435\u043c \u0440\u0430\u043d\u044c\u0448\u0435.<\/strong><\/p>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430:<\/p>\n<\/p>\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> \u0420\u0435\u0448\u0430\u0435\u043c \u0434\u043b\u044f \u043f\u043e\u043b\u043d\u043e\u043c\u043e\u0447\u0438\u0439:<\/p>\n<\/p>\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> \u0418 \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f:<\/p>\n<\/p>\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\"> \u041f\u0440\u0438\u043c\u0435\u0440 2<\/h3>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u0441\u043e\u0431\u0438\u0440\u0430\u0435\u043c\u0441\u044f \u0440\u0435\u0448\u0438\u0442\u044c \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u0443\u044e \u0437\u0430\u0434\u0430\u0447\u0443.<\/p>\n<ul>\n<li> \u041f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0430:<\/li>\n<\/ul>\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> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b:<\/p>\n<\/p>\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> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 n=3, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e:<\/p>\n<\/p>\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> \u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430:<\/p>\n<\/p>\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> \u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0430\u0435\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u0430\u0436\u043d\u043e \u0437\u0430\u043f\u043e\u043c\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0434\u0432\u0430 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430:<\/p>\n<p class=\"has-background\" style=\"background-color:#fffde7\"> \u2022 \u041a\u043e\u0433\u0434\u0430 \u043c\u043e\u043d\u043e\u043c \u0432\u043e\u0437\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f \u0432\u043e\u0437\u0432\u043e\u0434\u044f\u0442\u0441\u044f \u0432 \u043e\u0434\u043d\u0443 \u0438 \u0442\u0443 \u0436\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u2192<\/p>\n<\/p>\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> \u2022 \u041b\u044e\u0431\u043e\u0439 \u0447\u043b\u0435\u043d, \u0434\u043e\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0439 \u0434\u043e 0, \u0434\u0430\u0435\u0442 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> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043d\u0430\u0445\u043e\u0434\u0438\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0447\u0435\u0440\u0435\u0437 \u044d\u0442\u0438 \u0434\u0432\u0430 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430:<\/p>\n<\/p>\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 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> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0443\u043c\u043d\u043e\u0436\u0430\u0435\u043c \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435: <\/p>\n<\/p>\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\"><span class=\"ez-toc-section\" id=\"El-binomio-de-Newton-y-el-triangulo-de-Tartaglia-o-de-Pascal\"><\/span> \u0411\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 (\u0438\u043b\u0438 \u041f\u0430\u0441\u043a\u0430\u043b\u044f)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u0430\u043a \u0432\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0445 \u0432\u044b\u0448\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445, \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0443\u0442\u043e\u043c\u0438\u0442\u0435\u043b\u044c\u043d\u043e. \u0418\u043c\u0435\u043d\u043d\u043e \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0441\u043e\u0431\u0438\u0440\u0430\u0435\u043c\u0441\u044f \u043d\u0430\u0443\u0447\u0438\u0442\u044c \u0432\u0430\u0441 \u0442\u0440\u044e\u043a\u0443, \u0447\u0442\u043e\u0431\u044b \u0432\u0430\u043c \u043d\u0435 \u043f\u0440\u0438\u0445\u043e\u0434\u0438\u043b\u043e\u0441\u044c \u0440\u0435\u0448\u0430\u0442\u044c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e \u0443\u0437\u043d\u0430\u0442\u044c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043e\u043d\u0438 \u0441\u0442\u043e\u044f\u0442, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438, \u0442\u0430\u043a\u0436\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0439 \u043a\u0430\u043a \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u041f\u0430\u0441\u043a\u0430\u043b\u044f.<\/p>\n<p> \u0415\u0441\u043b\u0438 \u0432\u044b \u043d\u0435 \u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u044d\u0442\u043e \u0442\u0430\u043a\u043e\u0435, <strong>\u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438<\/strong> , \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u044b\u0439 <strong>\u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u043c \u041f\u0430\u0441\u043a\u0430\u043b\u044f<\/strong> , \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0447\u0438\u0441\u0435\u043b, \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u0445 \u0432 \u0444\u043e\u0440\u043c\u0435 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430.<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u0442\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 \u0438\u043b\u0438 \u041f\u0430\u0441\u043a\u0430\u043b\u044f, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043d\u0430\u0447\u0430\u0442\u044c \u0441 \u0432\u0435\u0440\u0448\u0438\u043d\u044b \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0432\u0441\u0435\u0433\u0434\u0430 \u0440\u0430\u0432\u043d\u0430 1, \u0430 \u0437\u0430\u0442\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u043e\u043c\u0435\u0440\u0430 \u0441\u0442\u0440\u043e\u043a \u043d\u0438\u0436\u0435. \u041a\u0430\u0436\u0434\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0432 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0441\u0442\u0440\u043e\u043a\u0430\u0445 \u0440\u0430\u0432\u043d\u043e \u0441\u0443\u043c\u043c\u0435 \u0434\u0432\u0443\u0445 \u0447\u0438\u0441\u0435\u043b, \u043d\u0430\u0445\u043e\u0434\u044f\u0449\u0438\u0445\u0441\u044f \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u043d\u0430\u0434 \u043d\u0438\u043c, \u0437\u0430 \u0438\u0441\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435\u043c \u043a\u043e\u043d\u0446\u043e\u0432 \u0441\u0442\u0440\u043e\u043a, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0432\u0441\u0435\u0433\u0434\u0430 \u0440\u0430\u0432\u043d\u044b 1. <\/p>\n<div class=\"wp-block-image\">\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=\"\u041d\u044c\u044e\u0442\u043e\u043d \u043f\u0430\u0440\u0430 1 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0448\u043a\u043e\u043b\u0430 \u043e\u043d\u043b\u0430\u0439\u043d\" class=\"wp-image-1936\" width=\"220\" height=\"288\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> \u0418\u0442\u0430\u043a, \u043a\u0430\u0436\u0434\u043e\u0435 \u0438\u0437 \u044d\u0442\u0438\u0445 \u0447\u0438\u0441\u0435\u043b \u0432 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0435 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0443 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430, \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0440\u0438\u0441\u0443\u043d\u043e\u043a: <\/p>\n<div class=\"wp-block-image\">\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> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442<\/p>\n<\/p>\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> \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e 3, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0435 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 \u043d\u0430 \u0435\u0433\u043e \u043f\u043e\u0437\u0438\u0446\u0438\u0438 \u0441\u0442\u043e\u0438\u0442 \u0446\u0438\u0444\u0440\u0430 3.<\/p>\n<p> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 (\u0438\u043b\u0438 \u041f\u0430\u0441\u043a\u0430\u043b\u044f) \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u0431\u044b\u0441\u0442\u0440\u0435\u0435, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d \u0438\u0437\u0431\u0430\u0432\u043b\u044f\u0435\u0442 \u043d\u0430\u0441 \u043e\u0442 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0435\u0441\u043b\u0438 \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u0430:<\/p>\n<\/p>\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> \u041f\u0440\u0438\u043c\u0435\u043d\u044f\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435:<\/p>\n<\/p>\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> \u0427\u0442\u043e \u0436, \u0432\u043c\u0435\u0441\u0442\u043e \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u043e\u0434\u043d\u043e \u0437\u0430 \u0434\u0440\u0443\u0433\u0438\u043c, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u043e\u0441\u0442\u043e \u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c \u043a\u0430\u0436\u0434\u043e\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u043c \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u043c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0431\u0438\u043d\u043e\u043c \u043f\u043e\u0434\u043d\u0438\u043c\u0430\u0435\u0442\u0441\u044f \u0434\u043e 3-\u0433\u043e \u0443\u0440\u043e\u0432\u043d\u044f, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u043d \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u0440\u0435\u0442\u044c\u0435\u043c\u0443 \u0443\u0440\u043e\u0432\u043d\u044e \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0422\u0430\u0440\u0442\u0430\u043b\u044c\u044f \u0438\u043b\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u041f\u0430\u0441\u043a\u0430\u043b\u044f \u0438 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430\" class=\"wp-image-2041\" width=\"319\" height=\"218\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\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> \u0418 \u0442\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u043c \u043e\u0441\u0442\u0430\u0451\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u043e\u0434\u0435\u043b\u0430\u0442\u044c \u043e\u0441\u0442\u0430\u0432\u0448\u0438\u0435\u0441\u044f \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438:<\/p>\n<\/p>\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 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> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 (\u0438\u043b\u0438 \u041f\u0430\u0441\u043a\u0430\u043b\u044f) \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u043c \u0438 \u0431\u044b\u0441\u0442\u0440\u044b\u043c \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u043c, \u043a\u0430\u043a \u043c\u044b \u043f\u043e\u043a\u0430\u0437\u0430\u043b\u0438. \u0418\u043c\u0435\u043d\u043d\u043e \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0443\u0435\u043c \u0435\u0433\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c.<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0434\u0432\u043e\u0434\u044f \u0438\u0442\u043e\u0433 \u0432\u0441\u0435\u043c\u0443, \u0447\u0442\u043e \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0434\u043e \u0441\u0438\u0445 \u043f\u043e\u0440, \u043c\u044b \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0430\u043c \u0438\u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0449\u0435\u0435, \u043a\u0430\u043a \u0432\u044b\u0433\u043b\u044f\u0434\u044f\u0442 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u043e\u0432 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0441 \u0447\u0438\u0441\u043b\u0430\u043c\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 (\u0438\u043b\u0438 \u041f\u0430\u0441\u043a\u0430\u043b\u044f): <\/p>\n<div class=\"wp-block-image\">\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=\"\u0411\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u041f\u0430\u0441\u043a\u0430\u043b\u044f \u0438\u043b\u0438 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u044f\" class=\"wp-image-2151\" width=\"535\" height=\"379\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-de-Newton-negativo-potencia-de-una-resta\"><\/span> \u041e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430: \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0414\u043e \u0441\u0438\u0445 \u043f\u043e\u0440 \u0432\u0441\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u0440\u0435\u0448\u0438\u043b\u0438, \u0431\u044b\u043b\u0438 \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043a\u043e\u0433\u0434\u0430 \u043e\u0434\u0438\u043d \u0438\u0437 \u0434\u0432\u0443\u0445 \u0447\u043b\u0435\u043d\u043e\u0432 \u0431\u0438\u043d\u043e\u043c\u0430 \u0438\u043c\u0435\u0435\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0437\u043d\u0430\u043a, \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0430 \u043e\u0441\u0442\u0430\u0435\u0442\u0441\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e\u0439, \u043d\u043e \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f.<\/p>\n<p class=\"has-background\" style=\"background-color:#ffebee\"> \u041a\u043e\u0433\u0434\u0430 \u043e\u0434\u0438\u043d \u0438\u0437 \u0447\u043b\u0435\u043d\u043e\u0432 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u0435\u043d, \u0442\u043e \u0435\u0441\u0442\u044c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435 \u0442\u0438\u043f\u0430 (ab) <sup>n<\/sup> , \u0437\u043d\u0430\u043a\u0438 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0434\u043e\u043b\u0436\u043d\u044b \u0447\u0435\u0440\u0435\u0434\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0432 \u0432\u0438\u0434\u0435 + \u2013 + \u2013 + \u2013 + \u2013 \u2026<\/p>\n<p> \u041d\u0438\u0436\u0435 \u043c\u044b \u0440\u0430\u0437\u0432\u0438\u043b\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0431\u0438\u043d\u043e\u043c\u043e\u0432 \u043f\u0435\u0440\u0432\u044b\u0445 5 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0438 \u0443\u0436\u0435 \u0438\u043c\u0435\u044e\u0449\u0438\u0445\u0441\u044f \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e \u043d\u0430\u0439\u0442\u0438 \u043d\u0443\u0436\u043d\u043e\u0435 \u0432\u0430\u043c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435: <\/p>\n<div class=\"wp-block-image\">\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=\"\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f 2\" class=\"wp-image-2147\" width=\"525\" height=\"387\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-del-binomio-de-Newton\"><\/span> \u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0438\u043c\u0435\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438:<\/p>\n<ul>\n<li> \u0420\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0432\u0441\u0435\u0433\u0434\u0430 \u0434\u0430\u0435\u0442 \u043d\u0430 \u043e\u0434\u0438\u043d \u0447\u043b\u0435\u043d \u0431\u043e\u043b\u044c\u0448\u0435, \u0447\u0435\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0431\u0438\u043d\u043e\u043c\u0430. \u0418\u043b\u0438, \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0434\u043b\u044f \u043f\u0430\u0440\u044b\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> \u043e\u043d\u0438 \u0437\u0430\u0442\u0440\u043e\u043d\u0443\u0442\u044b<\/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> \u0443\u0441\u043b\u043e\u0432\u0438\u044f.<\/li>\n<li> \u0421\u0438\u043b\u044b \u0441\u0442\u0438\u0445\u0438\u0438\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> \u041d\u0430\u0447\u043d\u0438\u0442\u0435 \u0441<\/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> \u0438 \u043e\u043d\u0438 \u0443\u043c\u0435\u043d\u044c\u0448\u0430\u044e\u0442\u0441\u044f, \u043f\u043e\u043a\u0430 \u043d\u0435 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442 0 \u0432 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u043c \u043a\u0432\u0430\u0440\u0442\u0430\u043b\u0435.<\/li>\n<li> \u0421\u0438\u043b\u044b \u0441\u0442\u0438\u0445\u0438\u0438\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> \u043e\u043d\u0438 \u0438\u0434\u0443\u0442 \u0432 \u0434\u0440\u0443\u0433\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438: \u043d\u0430\u0447\u0438\u043d\u0430\u044e\u0442\u0441\u044f \u0441 0 \u0438 \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0432\u0430\u044e\u0442\u0441\u044f, \u043f\u043e\u043a\u0430 \u043d\u0435 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442<\/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> \u0432 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0439 \u0441\u0440\u043e\u043a.<\/li>\n<li> \u0414\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0441\u0443\u043c\u043c\u0430 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438\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> \u0418<\/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> \u0440\u0430\u0432\u043d\u043e<\/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> \u041a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u043f\u0440\u0438 \u043f\u0435\u0440\u0432\u043e\u043c \u0447\u043b\u0435\u043d\u0435 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0432\u0441\u0435\u0433\u0434\u0430 \u0440\u0430\u0432\u0435\u043d 1 (\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439), \u0430 \u0432\u0442\u043e\u0440\u043e\u0439 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044e \u0431\u0438\u043d\u043e\u043c\u0430 (\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u043c\u0443 \u0438\u043b\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u043c\u0443). <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Calcular-el-termino-k-esimo-del-binomio-de-Newton\"><\/span> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 k-\u0439 \u0447\u043b\u0435\u043d \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0425\u043e\u0442\u044f \u044d\u0442\u043e \u043d\u0435\u043e\u0431\u044b\u0447\u043d\u043e, \u0438\u043d\u043e\u0433\u0434\u0430 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0441\u0442\u043e\u043b\u043a\u043d\u0443\u0442\u044c\u0441\u044f \u0441 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0430\u043c\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0432\u043c\u0435\u0441\u0442\u043e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043d\u0430\u0441 \u043f\u0440\u043e\u0441\u044f\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c k-\u0439 \u0447\u043b\u0435\u043d \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u0447\u043b\u0435\u043d, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0437\u0430\u043d\u0438\u043c\u0430\u0435\u0442 \u043f\u043e\u0437\u0438\u0446\u0438\u044e k.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0447\u043b\u0435\u043d, \u0437\u0430\u043d\u0438\u043c\u0430\u044e\u0449\u0438\u0439 \u043c\u0435\u0441\u0442\u043e k \u0432 \u0431\u0438\u043d\u043e\u043c\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0442\u043e\u0433\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0431\u0438\u043d\u043e\u043c \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c \u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435\u043c:<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u0435\u043d, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 k-\u0433\u043e \u0447\u043b\u0435\u043d\u0430 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/span><\/li>\n<\/ul>\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;\">\n<li> <span style=\"color:#000000;font-weight: normal;\">\u0415\u0441\u043b\u0438 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 k-\u0433\u043e \u0447\u043b\u0435\u043d\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/span><\/li>\n<\/ul>\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> \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u043d\u0430\u0439\u0434\u0435\u043c \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u044b\u0439 \u0447\u043b\u0435\u043d \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0430 5-\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438:<\/p>\n<\/p>\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> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u0431\u0438\u043d\u043e\u043c, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0438\u0439 \u0438\u0437 \u0441\u0443\u043c\u043c\u044b, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u043f\u0435\u0440\u0432\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443:<\/p>\n<\/p>\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> \u0417\u0430\u043c\u0435\u043d\u0438\u043c \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u043c\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u043c\u0438:<\/p>\n<\/p>\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> \u0418 \u0434\u0435\u043b\u0430\u0435\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438: <\/p>\n<\/p>\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 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 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> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u044b\u0439 \u0447\u043b\u0435\u043d \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0431\u0435\u0437 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u0438 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0432\u0441\u0435\u0445 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-binomio-de-Newton\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043b\u0438, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430, \u043c\u044b \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0432\u0430\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0441 \u0431\u0438\u043d\u043e\u043c\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f. \u0422\u0430\u043a\u0436\u0435 \u043f\u043e\u043c\u043d\u0438\u0442\u0435, \u0447\u0442\u043e \u043b\u044e\u0431\u044b\u0435 \u0432\u043e\u043f\u0440\u043e\u0441\u044b \u0438 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u043d\u0430\u043c \u0432 \u043a\u043e\u043c\u043c\u0435\u043d\u0442\u0430\u0440\u0438\u044f\u0445.<\/p>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u0420\u0430\u0437\u043b\u043e\u0436\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u0435\u043e\u0440\u0435\u043c\u0443: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u041d\u044c\u044e\u0442\u043e\u043d\u0430:<\/p>\n<\/p>\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\"> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0431\u0438\u043d\u043e\u043c \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c 3, \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0442\u0440\u0435\u0442\u0438\u0439 \u0443\u0440\u043e\u0432\u0435\u043d\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438, \u0447\u0442\u043e\u0431\u044b \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043f\u043e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u044b \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c 1 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0448\u043a\u043e\u043b\u0430\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\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\"> \u041c\u044b \u043e\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043b\u044f\u0435\u043c \u043f\u043e\u043b\u043d\u043e\u043c\u043e\u0447\u0438\u044f:<\/p>\n<\/p>\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\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0443\u043c\u043d\u043e\u0436\u0430\u0435\u043c: <\/p>\n<\/p>\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 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\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u043f\u043e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0430: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u041d\u044c\u044e\u0442\u043e\u043d\u0430:<\/p>\n<\/p>\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\"> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0431\u0438\u043d\u043e\u043c \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d \u0432 \u043a\u0443\u0431, \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0442\u0440\u0435\u0442\u0438\u0439 \u0443\u0440\u043e\u0432\u0435\u043d\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u041f\u0430\u0441\u043a\u0430\u043b\u044f, \u0447\u0442\u043e\u0431\u044b \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0443\u0437\u043d\u0430\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043f\u043e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u044b \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c 1 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0448\u043a\u043e\u043b\u0430\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\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\"> \u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043c\u043e\u043d\u043e\u043c\u043e\u0432:<\/p>\n<\/p>\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\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0434\u0435\u043b\u0430\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f: <\/p>\n<\/p>\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 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\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u0420\u0430\u0437\u0432\u0435\u0440\u043d\u0438\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u041d\u044c\u044e\u0442\u043e\u043d\u0430: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u041d\u044c\u044e\u0442\u043e\u043d\u0430. \u041d\u043e \u0442\u0430\u043a \u043a\u0430\u043a \u0432\u043d\u0443\u0442\u0440\u0438 \u0441\u043a\u043e\u0431\u043e\u043a \u0443 \u043d\u0430\u0441 \u0438\u0434\u0435\u0442 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435, \u0442\u043e \u043d\u0430\u0434\u043e \u0447\u0435\u0440\u0435\u0434\u043e\u0432\u0430\u0442\u044c \u0437\u043d\u0430\u043a\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e:<\/p>\n<\/p>\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\"> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0431\u0438\u043d\u043e\u043c \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0442\u0440\u043e\u0439\u043a\u0438, \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0442\u0440\u0435\u0442\u0438\u0439 \u0443\u0440\u043e\u0432\u0435\u043d\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438, \u0447\u0442\u043e\u0431\u044b \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043f\u043e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0440\u0435\u0448\u0435\u043d\u044b \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c 1 \u0441\u0440\u0435\u0434\u043d\u044f\u044f \u0448\u043a\u043e\u043b\u0430\" class=\"wp-image-2041\" width=\"281\" height=\"192\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\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\"> \u041c\u044b \u043e\u0441\u0443\u0449\u0435\u0441\u0442\u0432\u043b\u044f\u0435\u043c \u043f\u043e\u043b\u043d\u043e\u043c\u043e\u0447\u0438\u044f:<\/p>\n<\/p>\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\"> \u0418 \u0440\u0435\u0448\u0430\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435: <\/p>\n<\/p>\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 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\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0440\u0430\u0441\u0448\u0438\u0440\u0435\u043d\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041d\u0430\u0434\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u043e\u0431\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043d\u043e \u0442\u0430\u043a \u043a\u0430\u043a \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432 \u0441\u043a\u043e\u0431\u043a\u0430\u0445 \u0441\u0442\u043e\u0438\u0442 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435, \u0442\u043e \u043d\u0430\u0434\u043e \u0447\u0435\u0440\u0435\u0434\u043e\u0432\u0430\u0442\u044c \u0437\u043d\u0430\u043a\u0438 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e:<\/p>\n<\/p>\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\"> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0431\u0438\u043d\u043e\u043c \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d \u0432 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u0443\u044e \u0441\u0442\u0443\u043f\u0435\u043d\u044c, \u043c\u044b \u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0443\u0440\u043e\u0432\u0435\u043d\u044c 4 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0442\u043e\u0440\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430\" class=\"wp-image-2100\" width=\"296\" height=\"232\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\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\"> \u041c\u044b \u0440\u0435\u0430\u043b\u0438\u0437\u0443\u0435\u043c \u0432\u0441\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438:<\/p>\n<\/p>\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\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0440\u0435\u0448\u0430\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435: <\/p>\n<\/p>\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 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\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 5<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0441\u0435\u0434\u044c\u043c\u043e\u0439 \u0447\u043b\u0435\u043d \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u044d\u0442\u043e \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0431\u0438\u043d\u043e\u043c, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u0443:<\/p>\n<\/p>\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\"> \u041c\u044b \u0445\u043e\u0442\u0438\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0447\u043b\u0435\u043d 7, \u0438 \u0431\u0438\u043d\u043e\u043c \u0432\u043e\u0437\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c 10, \u043f\u043e\u044d\u0442\u043e\u043c\u0443, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u0432 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u0441\u044f:<\/p>\n<\/p>\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\"> \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0440\u0430\u0431\u043e\u0442\u044b \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0437\u043d\u0430\u0442\u044c \u0442\u0435\u0440\u043c\u0438\u043d: <\/p>\n<\/p>\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\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Historia-del-Binomio-de-Newton\"><\/span> \u0418\u0441\u0442\u043e\u0440\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0425\u043e\u0442\u044f \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u043f\u0440\u0438\u043f\u0438\u0441\u044b\u0432\u0430\u044e\u0442 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u043c\u0443 \u0430\u043d\u0433\u043b\u0438\u0439\u0441\u043a\u043e\u043c\u0443 \u0443\u0447\u0451\u043d\u043e\u043c\u0443 \u0418\u0441\u0430\u0430\u043a\u0443 \u041d\u044c\u044e\u0442\u043e\u043d\u0443 (1642-1727), \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u043f\u0435\u0440\u0432\u0430\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0438\u0440\u043e\u0432\u043a\u0430 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0431\u044b\u043b\u0430 \u0432\u043f\u0435\u0440\u0432\u044b\u0435 \u043e\u0442\u043a\u0440\u044b\u0442\u0430 \u043f\u0435\u0440\u0441\u0438\u0434\u0441\u043a\u0438\u043c \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u043e\u043c \u0410\u043b\u044c-\u041a\u0430\u0440\u0438\u0434\u0436\u0438 \u043e\u043a\u043e\u043b\u043e 1000 \u0433\u043e\u0434\u0430. \u0418 \u0434\u0430\u0436\u0435 \u0431\u044b\u043b\u043e \u043e\u0431\u043d\u0430\u0440\u0443\u0436\u0435\u043d\u043e, \u0447\u0442\u043e \u0412 XIII \u0432\u0435\u043a\u0435 \u043a\u0438\u0442\u0430\u0439\u0441\u043a\u0438\u0435 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u042f\u043d \u0425\u0443\u044d\u0439 \u0438 \u0427\u0443 \u0428\u0438-\u0427\u044c\u0435 \u0443\u0436\u0435 \u0437\u043d\u0430\u043b\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0430\u043b\u044b\u0445 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439.<\/p>\n<p> \u041f\u043e\u0437\u0436\u0435, \u0432 17 \u0432\u0435\u043a\u0435, \u041d\u044c\u044e\u0442\u043e\u043d \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430, \u0437\u0430\u043b\u043e\u0436\u0435\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u043c\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u043c\u0438, \u0440\u0430\u0441\u0448\u0438\u0440\u0438\u043b \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u0435\u043e\u0440\u0435\u043c\u0443. \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0440\u043f\u043e\u043b\u044f\u0446\u0438\u0438 \u0438 \u044d\u043a\u0441\u0442\u0440\u0430\u043f\u043e\u043b\u044f\u0446\u0438\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0414\u0436\u043e\u043d\u0430 \u0423\u043e\u043b\u043b\u0441\u0430, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438 \u043e\u0431\u043e\u0431\u0449\u0435\u043d\u043d\u044b\u0445 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0435\u0439, \u043e\u043d \u0441\u043c\u043e\u0433 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u044c \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0432 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0440\u044f\u0434.<\/p>\n<p> \u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u0432 1665 \u0433\u043e\u0434\u0443 \u041d\u044c\u044e\u0442\u043e\u043d\u0443 \u0443\u0434\u0430\u043b\u043e\u0441\u044c \u043f\u0440\u043e\u0434\u0435\u043c\u043e\u043d\u0441\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c n \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u0435\u043c, \u0442\u043e \u0435\u0441\u0442\u044c, \u0447\u0442\u043e \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0431\u0438\u043d\u043e\u043c\u0430 \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0430, \u0435\u0441\u043b\u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0434\u0440\u043e\u0431\u044c\u044e. \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u044d\u0442\u043e \u0431\u044b\u043b\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u043e \u0438 \u0432 \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044f. \u0418, \u0447\u0442\u043e \u0443\u0434\u0438\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u043d \u043e\u0431\u043d\u0430\u0440\u0443\u0436\u0438\u043b, \u0447\u0442\u043e \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439 \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0439 \u0440\u044f\u0434 \u0447\u043b\u0435\u043d\u043e\u0432.<\/p>\n<p> \u0418\u043c\u0435\u043d\u043d\u043e \u0441 \u044d\u0442\u0438\u043c \u043e\u0442\u043a\u0440\u044b\u0442\u0438\u0435\u043c \u041d\u044c\u044e\u0442\u043e\u043d \u043d\u0430\u0447\u0430\u043b \u043f\u043e\u0434\u0432\u0435\u0440\u0433\u0430\u0442\u044c \u0441\u043e\u043c\u043d\u0435\u043d\u0438\u044e \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u043c\u0438 \u0440\u044f\u0434\u0430\u043c\u0438 \u0438 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u043c\u0438 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u043c\u0438 \u0438 \u043f\u0440\u0438\u0448\u0435\u043b \u043a \u0432\u044b\u0432\u043e\u0434\u0443, \u0447\u0442\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u043c\u043e\u0433\u0443\u0442 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0442\u044c\u0441\u044f \u0441 \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u043c\u0438 \u0440\u044f\u0434\u0430\u043c\u0438 \u0442\u0430\u043a \u0436\u0435, \u043a\u0430\u043a \u0438 \u0441 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u043c\u0438 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f\u043c\u0438. \u0425\u043e\u0442\u044f \u041d\u044c\u044e\u0442\u043e\u043d \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u043f\u0443\u0431\u043b\u0438\u043a\u043e\u0432\u0430\u043b \u044d\u0442\u0443 \u0442\u0435\u043e\u0440\u0435\u043c\u0443, \u0414\u0436\u043e\u043d \u0423\u043e\u043b\u043b\u0441 \u0432 \u043a\u043e\u043d\u0446\u0435 \u043a\u043e\u043d\u0446\u043e\u0432 \u0441\u0434\u0435\u043b\u0430\u043b \u044d\u0442\u043e \u0432 1685 \u0433\u043e\u0434\u0443, \u043f\u0440\u0438\u043f\u0438\u0441\u0430\u0432 \u044d\u0442\u043e \u043e\u0442\u043a\u0440\u044b\u0442\u0438\u0435 \u041d\u044c\u044e\u0442\u043e\u043d\u0443.<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 (\u0438\u043b\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430) \u0438 \u043a\u0430\u043a\u043e\u0432\u0430 \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c, \u043a\u0430\u043a \u044d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0422\u0430\u0440\u0442\u0430\u043b\u044c\u0438 (\u0438\u043b\u0438 \u041f\u0430\u0441\u043a\u0430\u043b\u044f). \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0434\u043b\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u0438 \u0432\u0441\u0435\u0445 \u0435\u0433\u043e \u0441\u0432\u043e\u0439\u0441\u0442\u0432. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \u043a\u0443\u0440\u044c\u0435\u0437\u044b, \u043b\u0435\u0436\u0430\u0449\u0438\u0435 \u0432 \u043e\u0441\u043d\u043e\u0432\u0435 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d1%84%d0%be%d1%80%d0%bc%d1%83%d0%bb%d0%b0-%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b8-%d1%82%d0%b5%d0%be%d1%80%d0%b5%d0%bc%d1%8b-%d0%b8%d0%bb%d0%b8-%d0%b1%d0%b8%d0%bd\/\"> <span class=\"screen-reader-text\">\u0411\u0438\u043d\u043e\u043c \u043d\u044c\u044e\u0442\u043e\u043d\u0430 (\u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430)<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &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-66","post","type-post","status-publish","format-standard","hentry","category-2"],"yoast_head":"<!-- This site is optimized 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