{"id":322,"date":"2023-07-06T06:31:47","date_gmt":"2023-07-06T06:31:47","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%ab%8b%e6%96%b9\/"},"modified":"2023-07-06T06:31:47","modified_gmt":"2023-07-06T06:31:47","slug":"%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%ab%8b%e6%96%b9","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%ab%8b%e6%96%b9\/","title":{"rendered":"\u4e8c\u9879\u5f0f\u7acb\u65b9"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u627e\u5230\u4e8c\u9879\u5f0f\u4e09\u6b21\uff08\u516c\u5f0f\uff09\u7684\u91cd\u8981\u4e58\u79ef\uff08 (a+b) <sup>3<\/sup>\u6216 (ab) <sup>3<\/sup> \uff09\u5206\u8fa8\u7387\u7684\u8bf4\u660e\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u4ece\u4e8c\u9879\u5f0f\u5230\u7acb\u65b9\u4f53\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u548c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-binomio-al-cubo\"><\/span>\u4ec0\u4e48\u662f\u4e09\u6b21\u4e8c\u9879\u5f0f\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4e09\u6b21\u4e8c\u9879\u5f0f<\/strong>\u662f\u7531\u4e24\u9879 3 \u6b21\u65b9\u7ec4\u6210\u7684\u591a\u9879\u5f0f\u3002\u56e0\u6b64\uff0c\u4e09\u6b21\u4e8c\u9879\u5f0f\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u53ef\u4ee5\u662f<strong>(a+b) <sup>3<\/sup><\/strong>\u6216<strong>(ab) <sup>3<\/sup><\/strong> \uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u6211\u4eec\u662f\u6dfb\u52a0\u8fd8\u662f\u51cf\u53bb\u5b83\u4eec\u7684\u5355\u9879\u5f0f\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u4e09\u6b21\u4e8c\u9879\u5f0f\u662f\u663e\u7740\u6052\u7b49\u5f0f\uff08\u6216\u663e\u7740\u4e58\u79ef\uff09\u4e4b\u4e00\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u5b83\u5bf9\u5e94\u4e8e<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u6052\u7b49\u5f0f\u4ea7\u54c1-\u663e\u7740\u7684\u7b49\u5f0f\u89e3\u51b3\u7ec3\u4e60\/\">\u7acb\u65b9\u4f53\uff08\u6216\u7acb\u65b9\u4f53\uff09\u7684\u663e\u7740\u7279\u6027<\/a><\/span><\/strong>\u4e4b\u4e00\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-binomio-al-cubo\"><\/span>\u4e8c\u9879\u5f0f\u7acb\u65b9\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e8c\u9879\u5f0f\u7acb\u65b9\u7684\u5b9a\u4e49\u4e2d\u770b\u5230\u7684\uff0c\u8fd9\u79cd\u7c7b\u578b\u7684\u663e\u7740\u6052\u7b49\u5f0f\u53ef\u4ee5\u7531\u52a0\u6cd5\u6216\u51cf\u6cd5\u7ec4\u6210\u3002\u56e0\u6b64\uff0c\u8be5\u516c\u5f0f\u6839\u636e\u662f\u6b63\u4e8c\u9879\u5f0f\u8fd8\u662f\u8d1f\u4e8c\u9879\u5f0f\u800c\u7565\u6709\u4e0d\u540c\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5206\u522b\u67e5\u770b\u6bcf\u79cd\u60c5\u51b5\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cubo-de-una-suma\"><\/span>\u603b\u548c\u7684\u7acb\u65b9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5f53\u6c42\u548c\u7684\u7acb\u65b9\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u6c42\u548c\u7684\u7acb\u65b9\u7684\u516c\u5f0f\u6765\u8ba1\u7b97\u5b83\uff1a <\/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-dune-somme-ou-somme-au-cube-formule.png\" alt=\"\u7acb\u65b9\u548c\u516c\u5f0f\u7684\u4e8c\u9879\u5f0f\" class=\"wp-image-2810\" width=\"286\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u4e8c\u9879\u5f0f\u7684\u4e09\u6b21\u65b9\uff08\u52a0\u6cd5\uff09\u7b49\u4e8e\u7b2c\u4e00\u4e2a\u7684\u7acb\u65b9\uff0c\u52a0\u4e0a\u7b2c\u4e00\u4e2a\u7684\u5e73\u65b9\u7684\u4e09\u500d\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\uff0c\u52a0\u4e0a\u7b2c\u4e00\u4e2a\u7684\u4e09\u500d\u4e58\u4ee5\u7b2c\u4e8c\u4e2a\u7684\u5e73\u65b9\uff0c\u518d\u52a0\u4e0a\u7b2c\u4e8c\u4e2a\u7684\u7acb\u65b9\u3002<\/p>\n<p>\u8ba1\u7b97\u4e8c\u9879\u5f0f\u7acb\u65b9\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u725b\u987f\u4e8c\u9879\u5f0f\uff08\u6216\u4e8c\u9879\u5f0f\u5b9a\u7406\uff09\u3002\u6211\u4eec\u4e3a\u60a8\u7559\u4e0b\u4e86\u4ee5\u4e0b\u94fe\u63a5\u6765\u89e3\u91ca\u8be5\u5b9a\u7406\uff0c\u56e0\u4e3a\u4e86\u89e3\u8be5\u516c\u5f0f\u975e\u5e38\u6709\u7528\uff0c\u56e0\u4e3a\u5b83\u4e0d\u4ec5\u9002\u7528\u4e8e\u4e09\u6b21\u4e8c\u9879\u5f0f\u7684\u5e42\uff0c\u800c\u4e14\u9002\u7528\u4e8e\u66f4\u9ad8\u7684\u6307\u6570\u3002\u56e0\u6b64\uff0c\u5355\u51fb\u6b64\u94fe\u63a5\u5373\u53ef\u4e86\u89e3\u5e76\u80fd\u591f\u901a\u8fc7<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u4e8c\u9879\u5f0f\u6216\u725b\u987f\u4e8c\u9879\u5f0f\u5b9a\u7406\u516c\u5f0f\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\/\">\u5df2\u89e3\u51b3\u7684\u725b\u987f\u4e8c\u9879\u5f0f\u7ec3\u4e60<\/a><\/span><\/strong>\u8fdb\u884c\u7ec3\u4e60\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Cubo-de-una-diferencia\"><\/span>\u5dee\u5f02\u7684\u7acb\u65b9\u4f53<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u6211\u4eec\u4e0d\u662f\u6c42\u548c\uff0c\u800c\u662f\u6c42\u4e09\u6b21\u65b9\u7684\u5dee\uff08\u6216\u51cf\u6cd5\uff09\uff0c\u5219\u4e8c\u9879\u5f0f\u4e09\u6b21\u65b9\u7684\u516c\u5f0f\u4f1a\u6539\u53d8\u5076\u6570\u9879\u7684\u7b26\u53f7\uff1a <\/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-dune-soustraction-de-difference-de-la-formule-du-cube.png\" alt=\"\u7acb\u65b9\u516c\u5f0f\u7684\u5dee\u503c\u6216\u51cf\u6cd5\u7684\u4e8c\u9879\u5f0f\" class=\"wp-image-2811\" width=\"286\" height=\"286\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u4e8c\u9879\u5f0f\u7684\u4e09\u6b21\u65b9\uff08\u51cf\u6cd5\uff09\u7b49\u4e8e\u7b2c\u4e00\u4e2a\u7684\u7acb\u65b9\u51cf\u53bb\u7b2c\u4e8c\u4e2a\u7684\u4e09\u500d\u4e8e\u7b2c\u4e00\u4e2a\u7684\u5e73\u65b9\uff0c\u52a0\u4e0a\u7b2c\u4e00\u4e2a\u7684\u4e09\u500d\u5230\u7b2c\u4e8c\u4e2a\u7684\u5e73\u65b9\uff0c\u518d\u51cf\u53bb\u7b2c\u4e8c\u4e2a\u7684\u7acb\u65b9\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u548c\u7684\u7acb\u65b9\u4e0e\u5dee\u7684\u7acb\u65b9\u7684\u516c\u5f0f\u552f\u4e00\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\u7b2c\u4e8c\u9879\u548c\u7b2c\u56db\u9879\u7684\u7b26\u53f7\uff0c\u56e0\u4e3a\u5728\u548c\u7684\u4e8c\u9879\u5f0f\u4e2d\uff0c\u6240\u6709\u9879\u90fd\u662f\u6b63\u6570\uff0c\u76f8\u53cd\uff0c\u5728\u51cf\u6cd5\u7684\u4e8c\u9879\u5f0f\u90fd\u662f\u8d1f\u6570\u3002<\/p>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u4e86\u4ec0\u4e48\u662f\u4e8c\u9879\u5f0f\u548c\u548c\u4e8c\u9879\u5f0f\u5dee\u3002\u55ef\uff0c\u4f60\u5e94\u8be5\u77e5\u9053\uff0c\u4e24\u4e2a\u4e8c\u9879\u5f0f\u7684<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u548c\u4e0e\u5dee\u7684\u4e58\u79ef\u516c\u5f0f\/\">\u5dee<\/a><\/span><\/strong>\u548c\u4e5f\u662f\u4e00\u4e2a\u663e\u7740\u7684\u6052\u7b49\u5f0f\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u662f\u524d 3 \u4e2a\u6052\u7b49\u5f0f\u7684\u4e00\u90e8\u5206\uff08\u6700\u91cd\u8981\u7684\uff09\u3002\u60a8\u53ef\u4ee5\u67e5\u770b\u603b\u548c\u4e58\u4ee5\u5dee\u503c\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u4ee5\u53ca\u5982\u4f55\u5c06\u5176\u5e94\u7528\u5230\u94fe\u63a5\u9875\u9762\u4e0a\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-binomios-al-cubo\"><\/span>\u4e09\u6b21\u4e8c\u9879\u5f0f\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86\u548c\u7684\u7acb\u65b9\u7684\u516c\u5f0f\u4ee5\u53ca\u5dee\u7684\u7acb\u65b9\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u4e00\u4e2a\u6c42\u89e3\u6bcf\u79cd\u7c7b\u578b\u7684\u4e8c\u9879\u5f0f\u7acb\u65b9\u7684\u793a\u4f8b\u6765\u5b8c\u6210\u5bf9\u6982\u5ff5\u7684\u7406\u89e3\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-cubo-de-una-suma\"><\/span>\u603b\u548c\u7684\u7acb\u65b9\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u5c06\u4e8c\u9879\u5f0f\u6c42\u89e3\u4e3a\u4ee5\u4e0b\u7acb\u65b9\uff1a<\/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-9b6665bb45814802bf3d7dbb8b68c771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u4e8c\u9879\u5f0f\uff0c\u5176\u4e24\u9879\u5747\u4e3a\u6b63\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u7acb\u65b9\u548c\u7684\u516c\u5f0f\uff1a<\/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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u73b0\u5728\u9700\u8981\u627e\u5230\u53c2\u6570\u7684\u503c<\/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>\u548c<\/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>\u7684\u516c\u5f0f\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<\/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>\u5bf9\u5e94\u53d8\u91cf<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u548c<\/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>\u662f 2 \u53f7\u3002<\/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-909b3b4a2f976c165f160a6765b3ed9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a+b)^3\\\\[2ex] (x+2)^3 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x \\\\[2ex] b=2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"295\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u901a\u8fc7\u4ee3\u5165\u503c\u6765\u8ba1\u7b97\u4e8c\u9879\u5f0f\u7acb\u65b9<\/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>\u548c\u7684<\/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>\u5728\u516c\u5f0f\uff1a <\/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\/exemple-dun-binome-somme-et-difference-au-cube.jpg\" alt=\"\u548c\u5dee\u7acb\u65b9\u4e8c\u9879\u5f0f\u7684\u793a\u4f8b\" class=\"wp-image-2468\" width=\"419\" height=\"168\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-cubo-de-una-diferencia\"><\/span>\u5dee\u5f02\u7acb\u65b9\u4f53\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u4f7f\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u8ba1\u7b97\u4e0b\u4e00\u4e2a\u7acb\u65b9\u4e8c\u9879\u5f0f\uff08\u5dee\u503c\uff09\uff1a<\/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-fb0dbc34da8cea6a7d6622c9a3c5faba_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<p>\u5728\u672c\u7ec3\u4e60\u4e2d\uff0c\u6211\u4eec\u6709\u4e00\u5bf9\u5177\u6709\u6b63\u5143\u7d20\u548c\u8d1f\u5143\u7d20\u7684\u5143\u7d20\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u7acb\u65b9\u5dee\u7684\u516c\u5f0f\uff1a<\/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-746a96ec30fac619eedf62054c377fe5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3 = a^3-3a^2b+3ab^2 -b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\u6709\u5fc5\u8981\u786e\u5b9a\u672a\u77e5\u6570\u7684\u503c<\/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>\u548c<\/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>\u7684\u516c\u5f0f\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<\/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>\u8868\u793a\u5355\u9879\u5f0f 3x \u548c<\/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>\u662f\u4e8c\u9879\u5f0f\u7684\u72ec\u7acb\u9879\uff0c\u5373 2\u3002<\/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-a792ec6dead8466ec6a2cb2a43d9fab4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a-b)^3\\\\[2ex] (3x-2)^3 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=3x \\\\[2ex] b=2 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6ce8\u610f\u53c2\u6570<\/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-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>\u7b80\u5355\u5730\u7b49\u4e8e 2\uff0c\u6ca1\u6709\u6570\u5b57\u7684\u8d1f\u53f7\u3002\u8bb0\u4f4f\u8fd9\u4e00\u70b9\u5bf9\u4e8e\u6b63\u786e\u5e94\u7528\u8be5\u516c\u5f0f\u975e\u5e38\u91cd\u8981\u3002<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u901a\u8fc7\u5c06\u503c\u653e\u5165\u6765\u6c42\u89e3\u4e8c\u9879\u5f0f\u7acb\u65b9<\/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>\u548c\u7684<\/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>\u5728\u516c\u5f0f\uff1a <\/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-cube-negatif-parfait.jpg\" alt=\"\u8d1f\u5b8c\u7f8e\u7acb\u65b9\u4e8c\u9879\u5f0f\" class=\"wp-image-2476\" width=\"501\" height=\"169\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-del-binomio-al-cubo\"><\/span>\u4e8c\u9879\u5f0f\u7acb\u65b9\u516c\u5f0f\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u6f14\u793a\u4e09\u6b21\u4e8c\u9879\u5f0f\u7684\u516c\u5f0f\u3002\u867d\u7136\u663e\u7136\u6ca1\u6709\u5fc5\u8981\u4e86\u89e3\u5b83\uff0c\u4f46\u4e86\u89e3\u4efb\u4f55\u516c\u5f0f\u80cc\u540e\u7684\u4ee3\u6570\u603b\u662f\u6709\u597d\u5904\u7684\u3002<\/p>\n<p>\u4ece\u6b63\u7acb\u65b9\u4e8c\u9879\u5f0f\uff1a<\/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>\u4e0a\u9762\u7684\u8868\u8fbe\u5f0f\u53ef\u4ee5\u5728\u6570\u5b66\u4e0a\u5206\u89e3\u4e3a\u56e0\u5b50\u7684\u4e58\u79ef<\/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-2cfde4aacc08aae1ed70fe5f7b2f74de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u6309\u5176\u5e73\u65b9\uff1a<\/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-d89c1125bf18f5ec3b34a3bc8e4de45b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3=(a+b)\\cdot (a+b)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6b64\u5916\uff0c\u8fd9\u5bf9<\/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-2cfde4aacc08aae1ed70fe5f7b2f74de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u63d0\u9ad8\u5230 2 \u8fd9\u662f\u4e00\u4e2a\u663e\u7740\u7684\u6052\u7b49\u5f0f\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u7528<a href=\"https:\/\/mathority.org\/cn\/\u603b\u548c\u7684\u5e73\u65b9\u6216\u5e73\u65b9\u548c\/\"><strong><span style=\"text-decoration: underline;\">\u603b\u548c\u7684\u5e73\u65b9\u516c\u5f0f<\/span><\/strong><\/a>\u6765\u89e3\u51b3\u5b83\uff1a<\/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-4b1c6920425dd90a9526a1eaccf056b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)\\cdot (a+b)^2=(a+b)\\cdot (a^2+2ab+b^2)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"328\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u4f7f\u7528\u5206\u914d\u5f8b\u5c06\u4e24\u4e2a\u62ec\u53f7\u76f8\u4e58\uff1a<\/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-06771ecbb13542eae2a68477f849d729_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (a+b)\\cdot (a^2+2ab+b^2) &amp; = a\\cdot a^2 +a\\cdot 2ab + a\\cdot b^2+b\\cdot a^2 +b\\cdot 2ab +b \\cdot b^2 \\\\[2ex] &amp; = a^3+2a^2b+ab^2+ba^2+2ab^2+b^3 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"555\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u53ea\u9700\u5c06\u770b\u8d77\u6765\u76f8\u4f3c\u7684\u672f\u8bed\u5206\u7ec4\u5373\u53ef\uff1a<\/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-27d0da0e0e3ce760508c47f425fd1d68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^3+2a^2b+ab^2+ba^2+2ab^2+b^3 = a^3+3a^2b+3ab^2+b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"445\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p>\u5bf9\u4e8e\u8981\u9a8c\u8bc1\u7684\u4e09\u6b21\u4e8c\u9879\u5f0f\u7684\u516c\u5f0f\uff1a<\/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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u8981\u63a8\u5bfc\u51fa\u8d1f\u4e8c\u9879\u5f0f\u7acb\u65b9\u516c\u5f0f\uff0c\u8bf7\u9075\u5faa\u6211\u4eec\u521a\u521a\u6267\u884c\u7684\u76f8\u540c\u6b65\u9aa4\uff0c\u4f46\u4ece\u9879\u5f00\u59cb<\/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-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>\u6539\u53d8\u4e86\u6807\u5fd7\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u4e09\u6b21\u4e8c\u9879\u5f0f\u7684\u516c\u5f0f\u4e5f\u53ef\u4ee5\u4f7f\u7528<a href=\"https:\/\/mathority.org\/cn\/\u5854\u5854\u5229\u4e9a\u6216\u5e15\u65af\u5361\u4e09\u89d2\u5f62\/\"><strong><span style=\"text-decoration: underline;\">\u5e15\u65af\u5361\uff08\u6216\u5854\u5854\u5229\u4e9a\uff09\u4e09\u89d2\u5f62<\/span><\/strong><\/a>\u6765\u8bc1\u660e\u3002\u5982\u679c\u60a8\u4e0d\u77e5\u9053\u8fd9\u4e2a\u6570\u5b66\u6280\u5de7\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u4f1a\u4e3a\u60a8\u63d0\u4f9b\u6b64\u94fe\u63a5\uff0c\u5176\u4e2d\u5c06\u9010\u6b65\u8fdb\u884c\u89e3\u91ca\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5b83\u7684\u6240\u6709\u5e94\u7528\u4ee5\u53ca\u8fd9\u4e2a\u975e\u5e38\u7279\u6b8a\u7684\u4ee3\u6570\u4e09\u89d2\u5f62\u7684\u7279\u5b9a\u5386\u53f2\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-de-binomios-al-cubo\"><\/span>\u89e3\u51b3\u4e86\u4e8c\u9879\u5f0f\u7acb\u65b9\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u53ef\u4ee5\u7ec3\u4e60\u6211\u4eec\u521a\u521a\u770b\u5230\u7684\u5173\u4e8e\u8ba1\u7b97\u4e8c\u9879\u5f0f 3 \u6b21\u65b9\u7684\u7406\u8bba\uff0c\u6211\u4eec\u51c6\u5907\u4e86\u51e0\u4e2a\u9010\u6b65\u89e3\u51b3\u4e8c\u9879\u5f0f\u7acb\u65b9\u7684\u7ec3\u4e60\u3002<\/p>\n<p>\u6240\u4ee5\u4e0d\u8981\u5fd8\u8bb0\u544a\u8bc9\u6211\u4eec\u60a8\u5bf9\u8fd9\u4e2a\u89e3\u91ca\u7684\u770b\u6cd5\uff01\u60a8\u4e5f\u53ef\u4ee5\u5411\u6211\u4eec\u63d0\u51fa\u4efb\u4f55\u95ee\u9898\uff01 \ud83d\udc4d\ud83d\udc4d\ud83d\udc4d<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u6c42\u4e0b\u5217\u4e8c\u9879\u5f0f\u7684\u4e09\u6b21\u65b9\uff1a <\/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-ca75501df4056045f750323893bee27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x+4)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"88\" 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-f1ae5aad30adde91e86d6bb696b6adc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\left(x^2-5\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"100\" style=\"vertical-align: -7px;\"><\/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-debc2fbed1f43204a1d3b191ce697175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(2x-1\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" 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-641ad931932e2d32742c712339a76903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ (5x+2)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"97\" 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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u627e\u5230\u95ee\u9898\u7684\u6240\u6709\u663e\u7740\u6052\u7b49\u5f0f\uff0c\u53ea\u9700\u5c06\u4e8c\u9879\u5f0f\u516c\u5f0f\u5e94\u7528\u4e8e\u7acb\u65b9\u4f53\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u5b83\u662f\u52a0\u6cd5\u8fd8\u662f\u51cf\u6cd5\uff1a <\/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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-5a9a96bd2d1f115178fbbcf19c8047c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3 = a^3-3a^2b+3ab^2-b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-14695fb807e2df89352fdd1c1dced2ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}(x+4)^3&amp; =x^3+3\\cdot x^2\\cdot 4 +3\\cdot x\\cdot 4^2+4^3\\\\[2ex] &amp; =x^3+3\\cdot x^2\\cdot 4 +3\\cdot x\\cdot 16+64 \\\\[2ex] &amp; = \\bm{x^3+12x^2+48x+64}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"342\" style=\"vertical-align: 0px;\"><\/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-5be0d584351feb0bef5572ca5c9e159a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}\\left(x^2-5\\right)^3&amp; =\\left(x^2\\right)^3-3\\cdot \\left(x^2\\right)^2\\cdot 5 +3\\cdot x^2\\cdot 5^2-5^3\\\\[2ex] &amp; =x^6-3\\cdot x^4\\cdot 5 +3\\cdot x^2\\cdot 25-125 \\\\[2ex] &amp; = \\bm{x^6-15x^4+75x^2-125}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"110\" width=\"404\" style=\"vertical-align: 0px;\"><\/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-f44f9c3283dad97321644c6e559f64ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{aligned}\\left(2x-1\\right)^3&amp; =\\left(2x\\right)^3-3\\cdot \\left(2x\\right)^2\\cdot 1 +3\\cdot 2x\\cdot 1^2-1^3\\\\[2ex] &amp; =8x^3-3\\cdot 4x^2\\cdot 1 +3\\cdot 2x\\cdot 1-1 \\\\[2ex] &amp; = \\bm{8x^3-12x^2+6x-1}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"401\" style=\"vertical-align: 0px;\"><\/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-156e7619e4d6ef129f04250af8197d2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{aligned}(5x+2)^3&amp; =(5x)^3+3\\cdot \\left(5x\\right)^2\\cdot 2 +3\\cdot 5x\\cdot 2^2+2^3\\\\[2ex] &amp; =125x^3+3\\cdot 25x^2\\cdot 2 +3\\cdot 5x\\cdot 4+8 \\\\[2ex] &amp; = \\bm{125x^3+150x^2+60x+8}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"402\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u901a\u8fc7\u5e94\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u786e\u5b9a\u4ee5\u4e0b\u4e24\u4e2a\u91cf\u7684\u7acb\u65b9\u7684\u4e8c\u9879\u5f0f\uff1a <\/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-fa956af1cab818af1f22653b384dfc21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(4x^2-y^5\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"118\" style=\"vertical-align: -7px;\"><\/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-3a6734ab696568f02b53cc593ce70939_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(6x^3+2y^4\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"127\" style=\"vertical-align: -7px;\"><\/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-02817aca9c2bc6ddaf621c52a024719d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\left(\\frac{9}{2}x^2-\\frac{4}{3}x\\right)^3\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"137\" style=\"vertical-align: -17px;\"><\/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>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u8981\u8ba1\u7b97\u7ec3\u4e60\u4e2d\u6240\u6709\u91cd\u8981\u7684\u4e58\u79ef\uff0c\u60a8\u5fc5\u987b\u4f7f\u7528\u6c42\u548c\u548c\u7acb\u65b9\u51cf\u6cd5\u7684\u516c\u5f0f\uff1a <\/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-536cf8075ed9dc1e16eb5da114b79756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^3 = a^3+3a^2b+3ab^2 +b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-5a9a96bd2d1f115178fbbcf19c8047c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a-b)^3 = a^3-3a^2b+3ab^2-b^3\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"247\" 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-386169975ac336c1732a91ebd6d0830c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}\\left(4x^2-y^5\\right)^3&amp; =\\left(4x^2\\right)^3-3\\cdot \\left(4x^2\\right)^2\\cdot y^5 +3\\cdot 4x^2\\cdot \\left(y^5\\right)^2-\\left(y^5\\right)^3\\\\[2ex] &amp; =64x^6-3\\cdot 16x^4\\cdot y^5 +3\\cdot 4x^2\\cdot y^{10}-y^{15} \\\\[2ex] &amp; = \\bm{64x^6-48x^4y^5+12x^2y^{10}-y^{15}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"505\" style=\"vertical-align: 0px;\"><\/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-27c153bf59237b782cc697203d5f235a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}\\left(6x^3+2y^4\\right)^3&amp; =\\left(6x^3\\right)^3+3\\cdot \\left(6x^3\\right)^2\\cdot 2y^4 +3\\cdot 6x^3\\cdot \\left(2y^4\\right)^2+\\left(2y^4\\right)^3\\\\[2ex] &amp; =216x^9+3\\cdot 36x^6\\cdot 2y^4 +3\\cdot 6x^3\\cdot 4y^8+8y^{12} \\\\[2ex] &amp; = \\bm{216x^9+216x^6y^4 +72x^3y^8+8y^{12}}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"540\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\u4e00\u4e2a\u4e09\u6b21\u4e8c\u9879\u5f0f\u7684\u5355\u9879\u5f0f\u5177\u6709\u5206\u6570\u7cfb\u6570\uff0c\u56e0\u6b64\u8981\u89e3\u51b3\u5b83\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u5206\u6570\u7684\u6027\u8d28\uff1a <\/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-54262e17cdee07e9f36eb92f3b8b5727_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\begin{aligned}\\left(\\frac{9}{2}x^2-\\frac{4}{3}x\\right)^3 &amp; =\\left(\\frac{9}{2}x^2\\right)^3-3\\cdot \\left(\\frac{9}{2}x^2\\right)^2\\cdot \\frac{4}{3}x +3\\cdot \\frac{9}{2}x^2\\cdot \\left(\\frac{4}{3}x\\right)^2-\\left(\\frac{4}{3}x\\right)^3\\\\[3ex] &amp; =\\frac{9^3}{2^3}x^6-3\\cdot \\frac{9^2}{2^2}x^4\\cdot \\frac{4}{3}x +3\\cdot \\frac{9}{2}x^2\\cdot \\frac{4^2}{3^2}x^2-\\frac{4^3}{3^3}x^3 \\\\[3ex] &amp;= \\frac{729}{8}x^6-3\\cdot \\frac{81}{4}x^4\\cdot \\frac{4}{3}x +3\\cdot \\frac{9}{2}x^2\\cdot \\frac{16}{9}x^2-\\frac{64}{27}x^3 \\\\[3ex] &amp;= \\frac{729}{8}x^6-3\\cdot \\frac{324}{12}x^5 +3\\cdot \\frac{144}{18}x^4-\\frac{64}{27}x^3 \\\\[3ex] &amp;= \\frac{729}{8}x^6-3\\cdot 27x^5 +3\\cdot 8x^4-\\frac{64}{27}x^3 \\\\[3ex] &amp; = \\mathbf{\\frac{729}{8}}\\bm{x^6-81x^5 +24x^4-}\\mathbf{\\frac{64}{27}}\\bm{x^3}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"375\" width=\"589\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u8fd9\u91cc\uff0c\u60a8\u5c06\u627e\u5230\u4e8c\u9879\u5f0f\u4e09\u6b21\uff08\u516c\u5f0f\uff09\u7684\u91cd\u8981\u4e58\u79ef\uff08 (a+b) 3\u6216 (ab) 3 \uff09\u5206\u8fa8\u7387\u7684\u8bf4\u660e\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%ba%8c%e9%a1%b9%e5%bc%8f%e7%ab%8b%e6%96%b9\/\"> <span class=\"screen-reader-text\">\u4e8c\u9879\u5f0f\u7acb\u65b9<\/span> \u67e5\u770b\u5168\u6587 &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":[10],"tags":[],"class_list":["post-322","post","type-post","status-publish","format-standard","hentry","category-10"],"yoast_head":"<!-- This site is optimized 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