{"id":351,"date":"2023-07-06T01:29:47","date_gmt":"2023-07-06T01:29:47","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d1%8b\/"},"modified":"2023-07-06T01:29:47","modified_gmt":"2023-07-06T01:29:47","slug":"%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d1%8b","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d1%8b\/","title":{"rendered":"\u0411\u0438\u043d\u043e\u043c\u044b"},"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, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0431\u0438\u043d\u043e\u043c\u0430. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0441 \u0431\u0438\u043d\u043e\u043c\u0430\u043c\u0438: \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u043e\u0432, \u0431\u0438\u043d\u043e\u043c \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435, \u0431\u0438\u043d\u043e\u043c \u0432 \u043a\u0443\u0431\u0435,\u2026<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-binomio\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0430\u0440\u0430?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u0430\u043b\u0433\u0435\u0431\u0440\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/p>\n<p> <strong>\u0411\u0438\u043d\u043e\u043c \u2013 \u044d\u0442\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0438\u0439 \u0442\u043e\u043b\u044c\u043a\u043e \u0438\u0437 \u0434\u0432\u0443\u0445 \u043c\u043e\u043d\u043e\u043c\u043e\u0432<\/strong> . \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0431\u0438\u043d\u043e\u043c \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0435\u0433\u043e \u0432\u0441\u0435\u0433\u043e \u0438\u0437 \u0434\u0432\u0443\u0445 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432, \u0441\u043e\u0435\u0434\u0438\u043d\u0435\u043d\u043d\u044b\u0445 \u0437\u043d\u0430\u043a\u043e\u043c \u043f\u043b\u044e\u0441 (+) \u0438\u043b\u0438 \u0437\u043d\u0430\u043a\u043e\u043c \u043c\u0438\u043d\u0443\u0441 (-). <\/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.png\" alt=\"\u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0431\u0438\u043d\u043e\u043c\u044b\" class=\"wp-image-2992\" width=\"159\" height=\"159\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0421\u043b\u043e\u0432\u043e \u0431\u0438\u043d\u043e\u043c \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043e\u0442 \u0433\u0440\u0435\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u044f\u0437\u044b\u043a\u0430 \u0438 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0434\u0432\u0443\u0445 \u043b\u0435\u043a\u0441\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u043e\u0432 ( <em>bi<\/em> \u0438 <em>nomos<\/em> ), \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/p>\n<ul>\n<li> <em>bi<\/em> : \u043f\u0440\u0435\u0444\u0438\u043a\u0441, \u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0449\u0438\u0439 2.<\/li>\n<li> <em>\u043d\u043e\u043c\u043e\u0441<\/em> : \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442 \u0447\u0430\u0441\u0442\u044c.<\/li>\n<\/ul>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0432\u0435\u0441\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u0430: \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d\u0430 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0447\u0430\u0441\u0442\u0435\u0439 (\u0438\u043b\u0438 \u0434\u0432\u0443\u0445 \u043c\u043e\u043d\u043e\u043c\u043e\u0432).<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u043f\u043e\u043d\u044f\u0442\u0438\u0435 \u043f\u0430\u0440\u044b \u0438\u043c\u0435\u0435\u0442 \u0438\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435, \u0447\u0435\u043c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0435, \u0430 \u0438\u043c\u0435\u043d\u043d\u043e \u0442\u043e, \u0447\u0442\u043e \u043f\u0430\u0440\u0430 \u043c\u043e\u0436\u0435\u0442 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0442\u044c \u0438 \u0441\u043e\u0432\u043e\u043a\u0443\u043f\u043d\u043e\u0441\u0442\u044c \u0434\u0432\u0443\u0445 \u043b\u0438\u0447\u043d\u043e\u0441\u0442\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u043c \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0438\u0442 \u0432\u0435\u0434\u0443\u0449\u0430\u044f \u0440\u043e\u043b\u044c \u0432 \u043f\u043e\u043b\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0436\u0438\u0437\u043d\u0438, \u0432 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u0441\u043f\u043e\u0440\u0442\u0438\u0432\u043d\u044b\u0445 \u0434\u0438\u0441\u0446\u0438\u043f\u043b\u0438\u043d\u0430\u0445 \u0438\u043b\u0438 \u0434\u0430\u0436\u0435 \u0432 \u0441\u0444\u0435\u0440\u0435 \u0440\u0430\u0437\u0432\u043b\u0435\u0447\u0435\u043d\u0438\u0439. . \u041d\u043e, \u043e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u043c\u044b \u0441\u043e\u0441\u0440\u0435\u0434\u043e\u0442\u043e\u0447\u0438\u043c\u0441\u044f \u0437\u0434\u0435\u0441\u044c \u043d\u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u0431\u0438\u043d\u043e\u043c\u0430.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-binomios\"><\/span> \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0431\u0438\u043d\u043e\u043c\u043e\u0432<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0427\u0442\u043e\u0431\u044b \u0437\u0430\u0432\u0435\u0440\u0448\u0438\u0442\u044c \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0430, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0430 \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430:<\/p>\n<ul>\n<li> \u041f\u0440\u0438\u043c\u0435\u0440 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\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-05fba89f2955eb2762904c8527e26aa8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2+4x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"58\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041f\u0440\u0438\u043c\u0435\u0440 \u0431\u0438\u043d\u043e\u043c\u0430 \u0442\u0440\u0435\u0442\u044c\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438:<\/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-ae722155bf9498cffea4c08b7015fbee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3+5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"47\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041f\u0440\u0438\u043c\u0435\u0440 \u0431\u0438\u043d\u043e\u043c\u0430 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438:<\/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-0e6e322cb58245ab80d095c0a81fc631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x^4+8x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\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, \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0442\u0438\u043f\u044b \u0431\u0438\u043d\u043e\u043c\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442, \u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0441 \u0431\u0438\u043d\u043e\u043c\u0430\u043c\u0438.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-al-cuadrado\"><\/span> \u0431\u0438\u043d\u043e\u043c \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0411\u0438\u043d\u043e\u043c \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0437\u0430\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u043e, \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0435 \u0437\u0430\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u0438\u043b\u0438 \u0437\u0430\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e\u043c. \u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0431\u0438\u043d\u043e\u043c\u0430, \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u0433\u043e \u0432 2, \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0442\u043e\u0433\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d \u0431\u0438\u043d\u043e\u043c\u043e\u043c \u0441\u0443\u043c\u043c\u044b \u0438\u043b\u0438 \u0431\u0438\u043d\u043e\u043c\u043e\u043c \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438.<\/p>\n<p> \u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0441\u0443\u043c\u043c\u0430 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0441\u044f \u043a \u0442\u043e\u043c\u0443 \u0431\u0438\u043d\u043e\u043c\u0443, \u0434\u0432\u0430 \u0447\u043b\u0435\u043d\u0430 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b, \u0442\u043e \u0435\u0441\u0442\u044c \u0431\u0438\u043d\u043e\u043c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0439 \u0441\u0443\u043c\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-ef98ef741811c17cd99e75e5f848ea69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0431\u0438\u043d\u043e\u043c \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438 (\u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f) \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043e\u043f\u0440\u044f\u0436\u0435\u043d\u043d\u044b\u043c \u0431\u0438\u043d\u043e\u043c\u043e\u043c \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f, \u0442\u043e \u0435\u0441\u0442\u044c \u043e\u0434\u0438\u043d \u0438\u0437 \u0435\u0433\u043e \u043c\u043e\u043d\u043e\u043c\u043e\u0432 \u0438\u043c\u0435\u0435\u0442 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u0437\u043d\u0430\u043a. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/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-8f88949b2f3fcc20e9d00f495e471cf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0431\u0438\u043d\u043e\u043c\u0430, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u043a\u043e\u0442\u043e\u0440\u0430\u044f, \u043a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438, \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u0442\u043e\u0433\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u044d\u0442\u043e \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435\u043c \u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435\u043c. \u0423\u0437\u043d\u0430\u0439\u0442\u0435, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f, \u0432  <strong><span style=\"text-decoration: underline;\">\u0444\u043e\u0440\u043c\u0443\u043b\u0430\u0445 \u043f\u0440\u0438\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432<\/span><\/strong>  , \u0433\u0434\u0435 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0432\u0441\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u044b\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u044f, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f, \u043f\u0440\u0438\u0447\u0435\u043c \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u043f\u0440\u0438\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432, \u043d\u043e \u0438 \u0432\u0441\u0435\u0445 \u0438\u0445.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-al-cubo\"><\/span> \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0439 \u043a\u0443\u0431<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0425\u043e\u0442\u044f <strong>\u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u044b<\/strong> \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u0440\u0435\u0436\u0435, \u043e\u043d\u0438 \u0442\u0430\u043a\u0436\u0435 \u0441\u0447\u0438\u0442\u0430\u044e\u0442\u0441\u044f \u043f\u0440\u0438\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430\u043c\u0438. \u0418\u043b\u0438 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u0430, \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0449\u0438\u0435 \u0431\u044b\u0441\u0442\u0440\u043e \u043d\u0430\u0439\u0442\u0438 \u043a\u0443\u0431 \u0431\u0438\u043d\u043e\u043c\u0430 (\u0438\u0445 \u043c\u043e\u0436\u043d\u043e \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u043e \u0441\u0441\u044b\u043b\u043a\u0435 \u0432\u044b\u0448\u0435 <em><span style=\"text-decoration: underline;\">\u0444\u043e\u0440\u043c\u0443\u043b \u0437\u0430\u043c\u0435\u0442\u043d\u044b\u0445 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432<\/span><\/em> ).<\/p>\n<p> \u041a\u0430\u043a \u0438 \u0440\u0430\u043d\u044c\u0448\u0435, \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u044d\u0442\u043e\u0433\u043e \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u0442\u043e\u0433\u043e, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u043e\u043d \u043a\u0443\u0431\u043e\u043c \u0441\u0443\u043c\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-380239d5f1b18e11f3b6b0931a4f14d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0418\u043b\u0438, \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442, \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043a\u0443\u0431 \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438 \u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\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-6a48c875098bfee5d50068c1f0e7296d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041b\u043e\u0433\u0438\u0447\u043d\u043e, \u0447\u0442\u043e \u043e\u0441\u043d\u043e\u0432\u043d\u0430\u044f \u0440\u0430\u0437\u043d\u0438\u0446\u0430 \u043c\u0435\u0436\u0434\u0443 \u0431\u0438\u043d\u043e\u043c\u043e\u043c \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435 \u0438 \u0431\u0438\u043d\u043e\u043c\u043e\u043c \u0432 \u043a\u0443\u0431\u0435 \u2014 \u044d\u0442\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438. \u041e\u0434\u043d\u0430\u043a\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0430 \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u0441\u043b\u043e\u0436\u043d\u0435\u0435, \u0447\u0435\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0430.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomios-notables\"><\/span> \u0437\u0430\u043c\u0435\u0442\u043d\u044b\u0435 \u0441\u043e\u0433\u043b\u0430\u0448\u0435\u043d\u0438\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u0447\u0430\u0441\u0442\u043d\u043e\u0441\u0442\u0438, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0435 \u0442\u0438\u043f\u044b \u0431\u0438\u043d\u043e\u043c\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u0447\u043d\u044b \u0438\u0437-\u0437\u0430 \u0441\u0432\u043e\u0438\u0445 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0438 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0442 \u043c\u0435\u043d\u0435\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432\u0430\u043c (\u0438\u043b\u0438 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430\u043c).<\/p>\n<ul>\n<li> \u0421\u0443\u043c\u043c\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4609cf46d75484e45152fba69537c2ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\"><\/p>\n<\/li>\n<li> \u0420\u0430\u0437\u043d\u043e\u0441\u0442\u044c (\u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435) \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3e8c1ff5ed178c14d02192ff8c85b93b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2-b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li> \u0421\u0443\u043c\u043c\u0430 \u043a\u0443\u0431\u043e\u0432:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-945df8cc421a5647ed318b39d5e031f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3+b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -2px;\"><\/p>\n<\/li>\n<li> \u0420\u0430\u0437\u043d\u043e\u0441\u0442\u044c (\u0438\u043b\u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435) \u043a\u0443\u0431\u0438\u043a\u043e\u0432:\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-932403564d7ffe6622096bd031b4fd28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3-b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\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-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> \u2014 \u043b\u044e\u0431\u044b\u0435 \u0434\u0432\u0430 \u043c\u043e\u043d\u043e\u043c\u0430.<\/p>\n<p> \u0425\u043e\u0442\u044f \u044d\u0442\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u0445\u043e\u0436\u0438 \u043d\u0430 \u0442\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0447\u0443\u0442\u044c \u0432\u044b\u0448\u0435 (\u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0439 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0439 \u043a\u0443\u0431), \u0435\u0441\u043b\u0438 \u043f\u0440\u0438\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c\u0441\u044f, \u043e\u043d\u0438 \u043e\u0442\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f. \u0412 \u044d\u0442\u043e\u043c \u0441\u043c\u044b\u0441\u043b\u0435 \u0432\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u0438\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0431\u0438\u043d\u043e\u043c\u043e\u0432 \u0438 \u0438\u0445 \u0432\u044b\u0432\u043e\u0434\u044b, \u043d\u0430\u0436\u0430\u0432 \u043d\u0430 \u0441\u0441\u044b\u043b\u043a\u0443 \u0432\u044b\u0448\u0435 \u2b06 <em><span style=\"text-decoration: underline;\">\u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u0440\u0438\u043c\u0435\u0447\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0442\u043e\u0436\u0434\u0435\u0441\u0442\u0432.\u2b06<\/span><\/em> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Multiplicacion-de-binomios\"><\/span> \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041e\u0434\u043d\u043e\u0439 \u0438\u0437 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u044b\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0441 \u0431\u0438\u043d\u043e\u043c\u0430\u043c\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435. \u0418\u0442\u0430\u043a, \u0434\u0430\u043b\u0435\u0435 \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u0438\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-47234e6d6426b9822cf5b535eeb2d93f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x^2+2x)\\cdot (x-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"138\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0443\u043c\u043d\u043e\u0436\u0438\u0442\u044c \u043a\u0430\u0436\u0434\u044b\u0439 \u0447\u043b\u0435\u043d \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0431\u0438\u043d\u043e\u043c\u0430 \u043d\u0430 \u043a\u0430\u0436\u0434\u044b\u0439 \u0447\u043b\u0435\u043d \u0432\u0442\u043e\u0440\u043e\u0433\u043e \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-35c53275367a4876b719354ba10220a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^2\\cdot x+x^2\\cdot (-5)+2x\\cdot x +2x\\cdot (-5)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"283\" 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-8bac17566196aeb84f84fcabbec84ed0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x^3-5x^2+2x^2 -10x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"164\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p> \u0414\u0430\u043b\u0435\u0435 \u0433\u0440\u0443\u043f\u043f\u0438\u0440\u0443\u0435\u043c \u0441\u0445\u043e\u0436\u0438\u0435 \u0442\u0435\u0440\u043c\u0438\u043d\u044b, \u0442\u043e \u0435\u0441\u0442\u044c \u0438\u043c\u0435\u044e\u0449\u0438\u0435 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u0443\u044e \u0431\u0443\u043a\u0432\u0430\u043b\u044c\u043d\u0443\u044e \u0447\u0430\u0441\u0442\u044c:<\/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-6b1a70c63520e6d05a13d725480c7ba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{x^3-3x^2 -10x}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0418 \u0442\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c \u043d\u0430\u043c \u0443\u0434\u0430\u043b\u043e\u0441\u044c \u043d\u0430\u0439\u0442\u0438 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u043f\u0430\u0440\u0430\u043c\u0438. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Producto-de-dos-binomios-con-un-termino-comun\"><\/span> \u041f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0431\u0438\u043d\u043e\u043c\u043e\u0432 \u0441 \u043e\u0431\u0449\u0438\u043c \u0447\u043b\u0435\u043d\u043e\u043c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u041a\u043e\u0433\u0434\u0430 \u0431\u0438\u043d\u043e\u043c\u044b, \u0443\u0447\u0430\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0435 \u0432 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0438, \u0438\u043c\u0435\u044e\u0442 \u043e\u0431\u0449\u0438\u043c \u0447\u043b\u0435\u043d\u043e\u043c \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0443\u044e<\/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-038741496726a75b03e91a2e030b0287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0434\u043b\u044f \u0431\u044b\u0441\u0442\u0440\u043e\u0433\u043e \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u044d\u0442\u043e\u0439 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \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-0d402b74334bc5f53aec7f1ed85a2f5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+a)(x+b) = x^2+(a+b)x+ab\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"272\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0417\u0434\u0435\u0441\u044c \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0440\u0435\u0448\u0435\u043d\u043d\u043e\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u0443\u0432\u0438\u0434\u0435\u043b\u0438, \u043a\u0430\u043a \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u044d\u0442\u0443 \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-8447db6a2246c09b2e7be29f8050a3d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (x+4)(x+5) &amp;= x^2+(4+5)x+4\\cdot 5 \\\\[2ex] &amp; = x^2+9x+20 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"286\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Binomio-de-Newton\"><\/span> \u0411\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0411\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430<\/strong> , \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u044b\u0439 <strong>\u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u043e\u0439,<\/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, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0443\u044e \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0431\u0438\u043d\u043e\u043c\u043e\u0432. <\/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-73be038011b09c44860e6a3aac0ddeee_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}x^{n-k}y^k\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"206\" 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> \u041a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u044d\u0442\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0441\u043b\u043e\u0436\u043d\u043e \u043f\u043e\u043d\u044f\u0442\u044c. \u0412\u043e\u0442 \u043f\u043e\u0447\u0435\u043c\u0443 \u043c\u044b \u043f\u0440\u0438\u0432\u0435\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 \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, \"><\/figure>\n<\/div>\n<p> \u042d\u0442\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0443\u0442\u043e\u043c\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u0438\u043b\u0438 \u043a\u0443\u0431\u043e\u0432 \u0431\u0438\u043d\u043e\u043c\u043e\u0432, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443, \u043a\u0430\u043a \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0432\u044b\u0448\u0435, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b. \u041e\u0434\u043d\u0430\u043a\u043e \u0431\u0438\u043d\u043e\u043c \u041d\u044c\u044e\u0442\u043e\u043d\u0430 \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u043b\u0435\u0437\u0435\u043d \u0434\u043b\u044f \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u0431\u043e\u043b\u0435\u0435 \u0432\u044b\u0441\u043e\u043a\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043e\u043d \u0448\u0438\u0440\u043e\u043a\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0431\u0438\u043d\u043e\u043c\u0430 \u0447\u0435\u0442\u0432\u0435\u0440\u0442\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438.<\/p>\n<p> \u041d\u043e \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u044d\u0442\u0443 \u0444\u043e\u0440\u043c\u0443\u043b\u0443, \u0432\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0443\u043c\u0435\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\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 \u0442\u0438\u043f\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> , \u0440\u0430\u0441\u0447\u0435\u0442 \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e\u0439. \ud83d\udd0d <span style=\"text-decoration: underline;\">\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 \u0432\u0430\u043c \u043f\u043e\u0438\u0441\u043a\u0430\u0442\u044c, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f, \u0432 \u043d\u0430\u0448\u0435\u0439 \u043f\u043e\u0438\u0441\u043a\u043e\u0432\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0432\u0432\u0435\u0440\u0445\u0443 \u0441\u043f\u0440\u0430\u0432\u0430<\/span> \ud83d\udd0e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u043d\u0430\u0448\u0443 \u0441\u0442\u0430\u0442\u044c\u044e, \u0433\u0434\u0435 \u043c\u044b \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \u0432\u0430\u043c \u044d\u0442\u0443 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044e.<\/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, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0431\u0438\u043d\u043e\u043c\u0430. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0441 \u0431\u0438\u043d\u043e\u043c\u0430\u043c\u0438: \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u043e\u0432, \u0431\u0438\u043d\u043e\u043c \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435, \u0431\u0438\u043d\u043e\u043c \u0432 \u043a\u0443\u0431\u0435,\u2026 \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0430\u0440\u0430? \u0412 \u0430\u043b\u0433\u0435\u0431\u0440\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435: \u0411\u0438\u043d\u043e\u043c \u2013 \u044d\u0442\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0438\u0439 \u0442\u043e\u043b\u044c\u043a\u043e \u0438\u0437 \u0434\u0432\u0443\u0445 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d1%8b\/\"> <span class=\"screen-reader-text\">\u0411\u0438\u043d\u043e\u043c\u044b<\/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-351","post","type-post","status-publish","format-standard","hentry","category-2"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0411\u0438\u043d\u043e\u043c\u044b \u2014 \u043c\u0430\u0436\u043d\u043e\u0441\u0442\u044c<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ru\/\u0431\u0438\u043d\u043e\u043c\u044b\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0411\u0438\u043d\u043e\u043c\u044b \u2014 \u043c\u0430\u0436\u043d\u043e\u0441\u0442\u044c\" \/>\n<meta property=\"og:description\" content=\"\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, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u0431\u0438\u043d\u043e\u043c\u0430. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043c\u044b \u043f\u043e\u043a\u0430\u0436\u0435\u043c \u0432\u0430\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0441 \u0431\u0438\u043d\u043e\u043c\u0430\u043c\u0438: \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u043e\u0432, \u0431\u0438\u043d\u043e\u043c \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435, \u0431\u0438\u043d\u043e\u043c \u0432 \u043a\u0443\u0431\u0435,\u2026 \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0430\u0440\u0430? \u0412 \u0430\u043b\u0433\u0435\u0431\u0440\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0431\u0438\u043d\u043e\u043c\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435: \u0411\u0438\u043d\u043e\u043c \u2013 \u044d\u0442\u043e \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d, \u0441\u043e\u0441\u0442\u043e\u044f\u0449\u0438\u0439 \u0442\u043e\u043b\u044c\u043a\u043e \u0438\u0437 \u0434\u0432\u0443\u0445 &hellip; \u0411\u0438\u043d\u043e\u043c\u044b \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/ru\/\u0431\u0438\u043d\u043e\u043c\u044b\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T01:29:47+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/binome.png\" 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