{"id":318,"date":"2023-07-06T07:19:13","date_gmt":"2023-07-06T07:19:13","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%80%bb%e5%92%8c%e7%9a%84%e5%b9%b3%e6%96%b9%e6%88%96%e5%b9%b3%e6%96%b9%e5%92%8c\/"},"modified":"2023-07-06T07:19:13","modified_gmt":"2023-07-06T07:19:13","slug":"%e6%80%bb%e5%92%8c%e7%9a%84%e5%b9%b3%e6%96%b9%e6%88%96%e5%b9%b3%e6%96%b9%e5%92%8c","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%80%bb%e5%92%8c%e7%9a%84%e5%b9%b3%e6%96%b9%e6%88%96%e5%b9%b3%e6%96%b9%e5%92%8c\/","title":{"rendered":"\u603b\u548c\u7684\u5e73\u65b9\uff08\u6216\u5e73\u65b9\u548c\uff09"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u603b\u548c\u5e73\u65b9\u7684\u516c\u5f0f\uff0c\u5373\u8457\u540d\u7684\u6052\u7b49\u5f0f (a+b) <sup>2<\/sup> \u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u5e73\u65b9\u548c\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002\u800c\u4e14\uff0c\u66f4\u91cd\u8981\u7684\u662f\uff0c\u60a8\u4f1a\u53d1\u73b0\u9690\u85cf\u5728\u8fd9\u6b3e\u975e\u51e1\u4ea7\u54c1\u4e2d\u7684\u51e0\u4f55\u7279\u6027\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-cuadrado-de-una-suma\"><\/span>\u603b\u548c\u7684\u5e73\u65b9\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u548c\u7684\u5e73\u65b9<\/strong>\u662f\u503c\u5f97\u6ce8\u610f\u7684\u6052\u7b49\u5f0f\uff08\u6216\u503c\u5f97\u6ce8\u610f\u7684\u4e58\u79ef\uff09\u4e4b\u4e00\uff0c\u56e0\u6b64\u5b83\u662f\u4e00\u79cd\u6570\u5b66\u89c4\u5219\uff0c\u53ef\u8ba9\u60a8\u5feb\u901f\u8ba1\u7b97\u5177\u6709\u4e24\u4e2a\u6b63\u9879\u5e73\u65b9\u7684\u4e8c\u9879\u5f0f\u7684\u5e42\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u548c\u7684\u5e73\u65b9\u7531\u4e24\u4e2a\u4e0d\u540c\u7684\u9879\u76f8\u52a0\u5e76\u5e73\u65b9\u800c\u6210\uff0c\u5373\u548c\u7684\u5e73\u65b9\u7684\u4ee3\u6570\u8868\u8fbe\u5f0f\u4e3a<strong>(a+b) <sup>2<\/sup><\/strong> \u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-cuadrado-de-una-suma\"><\/span>\u603b\u548c\u7684\u5e73\u65b9\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u8fd9\u79cd\u975e\u51e1\u7c7b\u578b\u7684\u6052\u7b49\u5f0f\u7684\u6570\u5b66\u5b9a\u4e49\uff0c\u6211\u4eec\u73b0\u5728\u5c06\u4e86\u89e3<strong>\u603b\u548c\u5e73\u65b9\u7684\u516c\u5f0f<\/strong>\u662f\u4ec0\u4e48\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\/formule-pour-le-carre-dune-somme.png\" alt=\"\u603b\u548c\u7684\u5e73\u65b9\u516c\u5f0f\" class=\"wp-image-2339\" width=\"269\" height=\"270\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u56e0\u6b64\uff0c\u603b\u548c\u7684\u5e73\u65b9\u7b49\u4e8e\u7b2c\u4e00\u9879\u7684\u5e73\u65b9\uff0c\u52a0\u4e0a\u7b2c\u4e00\u9879\u4e0e\u7b2c\u4e8c\u9879\u4e58\u79ef\u7684\u4e24\u500d\uff0c\u518d\u52a0\u4e0a\u7b2c\u4e8c\u9879\u7684\u5e73\u65b9\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u6c42\u89e3\u5e73\u65b9\u548c\uff0c\u5c06\u6bcf\u4e2a\u52a0\u6cd5\u589e\u52a0\u5230 2 \u662f\u4e0d\u591f\u7684\uff0c\u6b64\u5916\uff0c\u8fd8\u5fc5\u987b\u5c06\u4e24\u4e2a\u52a0\u6cd5\u76f8\u4e58\u5e76\u4e58\u4ee5 2\u3002<\/p>\n<p>\u8bb0\u4f4f\u8fd9\u4e00\u70b9\u5f88\u91cd\u8981\uff0c\u56e0\u4e3a\u5728\u6dfb\u52a0\u5e73\u65b9\u65f6\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\u9519\u8bef\u662f\u5fd8\u8bb0\u4e24\u9879\u4e4b\u95f4\u7684\u4e58\u79ef\u800c\u53ea\u8ba1\u7b97\u5e73\u65b9\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\/polynomes-au-carre-dune-somme.jpg\" alt=\"\u591a\u9879\u5f0f\u548c\u7684\u5e73\u65b9\" class=\"wp-image-2342\" width=\"246\" height=\"68\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u8bf7\u8bb0\u4f4f\u4e0d\u8981\u5728\u516c\u5f0f\u4e2d\u9057\u6f0f\u4efb\u4f55\u9879\uff01<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u8bf7\u8bb0\u4f4f\uff0c\u5e73\u65b9\u51cf\u6cd5\uff08\u6216\u51cf\u6cd5\u7684\u5e73\u65b9\uff09\u7684\u516c\u5f0f\u4e0e\u6211\u4eec\u521a\u521a\u770b\u5230\u7684\u516c\u5f0f\u975e\u5e38\u76f8\u4f3c\uff0c\u4f46\u5b83\u6709\u4e00\u4e2a\u5dee\u5f02\uff0c\u5b8c\u5168\u6539\u53d8\u4e86\u7ed3\u679c\u3002\u5982\u679c\u60a8\u4e0d\u786e\u5b9a\u5b83\u662f\u4ec0\u4e48\u6837\u7684\uff0c\u60a8\u53ef\u4ee5\u5728\u6b64\u5904\u67e5\u770b<strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/cn\/\u5dee\u503c\u6216\u51cf\u6cd5\u7684\u5e73\u65b9\/\">\u5e73\u65b9\u51cf\u6cd5<\/a><\/span><\/strong>\u516c\u5f0f\u662f\u4ec0\u4e48\u53ca\u5176\u5e94\u7528\u65b9\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-cuadrados-de-sumas\"><\/span>\u5e73\u65b9\u548c\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4ee5\u4e0b\u662f\u51e0\u4e2a\u5b9e\u9645\u793a\u4f8b\uff0c\u60a8\u53ef\u4ee5\u4e86\u89e3\u5982\u4f55\u6c42\u548c\u7684\u5e73\u65b9\uff1a<\/p>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b1<\/h3>\n<ul>\n<li>\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u4ee5\u4e0b\u5e73\u65b9\u548c\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-9a9b2aa575ef7fa83e8bb98cbb385ac8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x+5)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"61\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5e73\u65b9\u548c\u7684\u516c\u5f0f\u4e3a\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-e3c7bb69fbb939444db4e075615462f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2=a^2+2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u9996\u5148\u8981\u786e\u5b9a\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-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>\u4ee3\u8868<\/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>\u7684\u5bf9\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>\u5bf9\u5e94\u6570\u5b575\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-5ba75b0f34f956985ea0163011a03acf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{l} (a+b)^2\\\\[2ex] (x+5)^2 \\end{array} \\color{red} \\right\\} \\quad \\color{red}\\bm{\\longrightarrow}\\quad  \\color{black} \\begin{array}{c} a=x \\\\[2ex] b=5 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"295\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u597d\u5427\uff0c\u65e2\u7136\u6211\u4eec\u73b0\u5728\u77e5\u9053\u4e86<\/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-a521efcd0a946cd643aebe98b5b41a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u6c42\u51fa\u603b\u548c\u5e73\u65b9\u7684\u7ed3\u679c\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\/produits-notables-au-carre-dune-somme.jpg\" alt=\"\u603b\u548c\u7684\u5e73\u65b9 \u8457\u540d\u4ea7\u54c1\" class=\"wp-image-2349\" width=\"284\" height=\"164\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\">\u5b9e\u65bd\u4f8b2<\/h3>\n<ul>\n<li>\u6c42\u89e3\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u4ee5\u83b7\u5f97\u603b\u548c\u7684\u5e73\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-12067275e14b98d59e004045606f26fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3x+4)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"70\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u603b\u548c\u5e73\u65b9\u7684\u516c\u5f0f\u4e3a\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-e3c7bb69fbb939444db4e075615462f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2=a^2+2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u90a3\u4e48\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d<\/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>\u662f\u5355\u9879\u5f0f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c<\/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\u72ec\u7acb\u9879 4\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-89bb3514fbd79ba368588655e152e9cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} a=3x \\\\[2ex] b=4 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"52\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u4e00\u65e6\u6211\u4eec\u786e\u5b9a\u4e86<\/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>\uff0c\u6211\u4eec\u5e94\u7528\u5e73\u65b9\u548c\u516c\u5f0f\u6765\u6c42\u89e3\u663e\u7740\u4e58\u79ef\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-ed0d9fcdbeeac2247b68789dd0268f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (3x+4)^2 &amp; =(3x)^2+2 \\cdot 3x\\cdot 4+4^2 \\\\[2ex] &amp; =9x^2+24x+16 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"256\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Demostracion-de-la-formula-del-cuadrado-de-una-suma\"><\/span>\u603b\u548c\u5e73\u65b9\u516c\u5f0f\u7684\u8bc1\u660e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7136\u540e\u6211\u4eec\u4f1a\u4ece\u548c\u7684\u5e73\u65b9\u63a8\u5bfc\u51fa\u521a\u624d\u770b\u5230\u7684\u516c\u5f0f\uff0c\u8fd9\u6837\u4f60\u5c31\u660e\u767d\u5b83\u662f\u4ece\u54ea\u91cc\u6765\u7684\u3002<\/p>\n<p>\u4ece\u6b63\u4e8c\u9879\u5f0f\u5f00\u59cb\u5230 2\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-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>\u4e0a\u9762\u7684\u5e42\u663e\u7136\u5c31\u7b49\u4e8e\u56e0\u5b50<\/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>\u4e58\u4ee5\u81ea\u8eab\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-7b2df207ac593eaf04ac60ac40b89a7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2=(a+b)\\cdot (a+b)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"200\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\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-1c871c4ad6546c817128379acbef78c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (a+b)\\cdot (a+b) &amp; = a\\cdot a +a\\cdot b +b\\cdot a +b\\cdot b \\\\[2ex] &amp;=a^2+ab+ba+b^2 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"325\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6839\u636e\u7ed3\u679c\u672f\u8bed\uff0c\u6211\u4eec\u5c06\u76f8\u4f3c\u7684\u672f\u8bed\u5206\u7ec4\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-b645fb320040c599e077b3e5bdc4b407_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2+ab+ba+b^2 = a^2+2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"256\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p>\u5e76\u4e14\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86\u8be5\u516c\u5f0f\u7684\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\uff0c\u56e0\u6b64\u8bc1\u660e\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-66c4071b50f376018a8ac9b6f3f9f5fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2= a^2+2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u5c3d\u7ba1\u53ef\u80fd\u96be\u4ee5\u7f6e\u4fe1\uff0c\u4f46\u6c42\u548c\u516c\u5f0f\u7684\u5e73\u65b9\u4e5f\u9002\u7528\u4e8e<a href=\"https:\/\/mathority.org\/cn\"><strong><span style=\"text-decoration: underline;\">\u4e8c\u6b21\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3<\/span><\/strong><\/a>\u3002\u5982\u679c\u60a8\u4e0d\u77e5\u9053\u5b83\u662f\u4ec0\u4e48\uff0c\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u662f\u6570\u5b66\u4e2d\u7ecf\u5e38\u7528\u4e8e\u7b80\u5316\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\u7684\u8fc7\u7a0b\u3002\u5355\u51fb\u4e0a\u9762\u7684\u94fe\u63a5\u4e86\u89e3\u5176\u64cd\u4f5c\u65b9\u6cd5\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interpretacion-geometrica-del-cuadrado-de-una-suma\"><\/span>\u603b\u548c\u5e73\u65b9\u7684\u51e0\u4f55\u89e3\u91ca<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u5982\u4f55\u7528\u6570\u5b66\u65b9\u6cd5\u8ba1\u7b97\u603b\u548c\u7684\u5e73\u65b9\uff0c\u4f46\u8fd9\u4e2a\u975e\u51e1\u7684\u4e58\u79ef\u4e5f\u53ef\u4ee5\u7528\u51e0\u4f55\u65b9\u6cd5\u6765\u89e3\u91ca\u3002<\/p>\n<p>\u770b\u4e0b\u9762\u7684\u6b63\u65b9\u5f62\uff0c\u5176\u8fb9\u957f\u662f\u591a\u5c11<\/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-5f03f5d7b3d514b94a628f988975c108_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a+b:\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -2px;\"><\/p>\n<\/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\/carre-geometrique-interpretation-d-une-somme.jpg\" alt=\"\u548c\u7684\u5e73\u65b9\u51e0\u4f55\u89e3\u91ca\" class=\"wp-image-2364\" width=\"282\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u65b9\u5f62\u7684\u9762\u79ef\u7b49\u4e8e\u5176\u4e00\u6761\u8fb9\u7684\u957f\u5ea6\u7684\u5e73\u65b9\u3002\u56e0\u6b64\uff0c\u7531\u4e8e\u524d\u4e00\u4e2a\u6b63\u65b9\u5f62\u7684\u8fb9\u662f<\/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-45dc37f5e6c04130e5e7cdc375a9fc8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a+b,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u5b83\u7684\u9762\u79ef\uff08\u6216\u8868\u9762\u79ef\uff09\u7b49\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b02b123bc26be5152c4a9917a6cb9539_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"63\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u55ef\uff0c\u6b63\u5982\u60a8\u5728\u6b63\u65b9\u5f62\u8868\u793a\u4e2d\u770b\u5230\u7684\uff0c\u9762\u79ef\u4e3a<\/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-d3fbbc716a20a1a8e5fb339ee863ef14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a^2,\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u6709\u4e24\u4e2a\u533a\u57df\u7684\u77e9\u5f62<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8d53cd0a9beed89b01eb3a3d6b7ff79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"ab,\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u548c\u53e6\u4e00\u4e2a\u6b63\u65b9\u5f62\u7684\u8868\u9762<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c3a795dbae63ac6ae2905fa73468f6dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b^2.\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u56e0\u6b64\uff0c\u4ece\u51e0\u4f55\u89d2\u5ea6\u6765\u770b\uff0c\u5e73\u65b9\u548c\u7684\u516c\u5f0f\u4e5f\u6210\u7acb\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-e3c7bb69fbb939444db4e075615462f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2=a^2+2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-cuadrado-de-una-suma\"><\/span>\u89e3\u51b3\u4e86\u603b\u548c\u7684\u5e73\u65b9\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7136\u540e\uff0c\u6211\u4eec\u7ed9\u60a8\u63d0\u4f9b\u51e0\u4e2a\u5df2\u89e3\u51b3\u7684\u5e73\u65b9\u548c\u9010\u6b65\u7ec3\u4e60\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u7ec3\u4e60\u5e76\u4ece\u800c\u5b8c\u6210\u5bf9\u6982\u5ff5\u7684\u7406\u89e3\u3002\u60a8\u53ef\u4ee5\u5728\u8bc4\u8bba\u4e2d\u5199\u4e0b\u60a8\u7684\u6240\u6709\u95ee\u9898\uff0c\u6211\u4eec\u5c06\u5f88\u4e50\u610f\u56de\u7b54\u3002 \ud83d\udcad\ud83d\udcad\ud83d\udcad<\/p>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u786e\u5b9a\u4ee5\u4e0b\u5e73\u65b9\u548c\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-9229e4ae2034182594cea6b72883a61e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ (x+3)^2\" 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-e9db6436020d25d8dde919b5db5071d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ (2+6x)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"96\" 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-55d230fdf4d87dfb39f5427089c4bcd0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\left(x^2+7\\right)^2\" 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-8858ec9b4957c47679e682ab433bd75d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ (5x+8y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" 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\">\u4e3a\u4e86\u89e3\u51b3\u95ee\u9898\u7684\u6240\u6709\u663e\u7740\u6052\u7b49\u5f0f\uff0c\u5e94\u7528\u603b\u548c\u5e73\u65b9\u516c\u5f0f\u5c31\u8db3\u591f\u4e86\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-e3c7bb69fbb939444db4e075615462f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2=a^2+2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" 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-571dada676a093b9b625887a09615b5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}(x+3)^2&amp; =x^2+2\\cdot x\\cdot 3 +3^2\\\\[2ex] &amp; = \\bm{x^2+6x +9}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"248\" 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-8d696f9e8ea8a9246922a0aa132d7e24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}(2+6x)^2 &amp; =2^2+2\\cdot 2\\cdot 6x +(6x)^2\\\\[2ex] &amp; = \\bm{4+24x+36x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"288\" 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-62f7ef68fc47d45958f6a10dbfe3f512_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\begin{aligned}\\left(x^2+7\\right)^2 &amp; = \\left(x^2\\right)^2+2\\cdot x^2\\cdot 7 +7^2\\\\[2ex] &amp; = \\bm{x^4+14x^2 +49}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"66\" width=\"290\" 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-2fdf798e7d585cdbc2bbeb0417bfc62a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{D)} \\ \\begin{aligned}(5x+8y)^2 &amp; =(5x)^2+2\\cdot 5x\\cdot 8y +(8y)^2\\\\[2ex] &amp; = \\bm{25x^2+80xy+64y^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"331\" 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>\u5e94\u7528\u4ee5\u4e0b\u516c\u5f0f\u6c42\u89e3\u4ee5\u4e0b\u4e24\u9879\u7684\u5e73\u65b9\u548c\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-cde71610badce0bddaa952e68411ea3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\left(4x^2+2y^3\\right)^2\" 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-097f1d298bc8e31ba41fc8163e310c6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\displaystyle \\left(\\sqrt{2x}+\\sqrt{8x}\\right)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"146\" style=\"vertical-align: -11px;\"><\/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-b432940794af539924a002fac6533134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\left(\\frac{4}{3}x^2+\\frac{3}{2}x\\right)^2\" 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\u95ee\u9898\u7684\u6240\u6709\u663e\u7740\u4e58\u79ef\uff0c\u60a8\u5fc5\u987b\u4f7f\u7528\u5e73\u65b9\u548c\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-e3c7bb69fbb939444db4e075615462f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(a+b)^2=a^2+2ab+b^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"184\" 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-b8eaa03c68adc376819c5e12081f6d39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{A)} \\ \\begin{aligned}\\left(4x^2+2y^3\\right)^2 &amp; =\\left(4x^2\\right)^2+2\\cdot 4x^2\\cdot 2y^3 +\\left(2y^3\\right)^2\\\\[2ex] &amp; = \\bm{16x^4+16x^2y^3+4y^6}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"68\" width=\"384\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u5728 B) \u90e8\u5206\u4e2d\uff0c\u60a8\u9700\u8981\u8bb0\u4f4f\uff0c\u5982\u679c\u6839\u662f\u5e73\u65b9\u7684\uff0c\u5219\u5b83\u4f1a\u88ab\u7b80\u5316\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-a38b1df7ca331cb002253d52eb008608_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{B)} \\ \\begin{aligned}\\left(\\sqrt{2x}+\\sqrt{8x}\\right)^2 &amp; =\\left(\\sqrt{2x}\\right)^2+2\\cdot \\sqrt{2x}\\cdot \\sqrt{8x} +\\left(\\sqrt{8x}\\right)^2\\\\[2ex] &amp; =2x+2\\sqrt{2x\\cdot 8x} +8x \\\\[2ex] &amp; = 10x+2\\sqrt{16x^2} \\\\[2ex] &amp;= 10x+2\\cdot 4x = \\\\[2ex] &amp; = 10x +8x \\\\[2ex] &amp; = \\bm{18x}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"247\" width=\"443\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\u4e00\u4e2a\u5e73\u65b9\u548c\u7684\u5355\u9879\u5f0f\u6709\u5206\u6570\u7cfb\u6570\uff0c\u56e0\u6b64\u8981\u89e3\u51b3\u5b83\uff0c\u6211\u4eec\u8fd8\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-c50dcca740e334b34f746e71f4af826e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{C)} \\ \\displaystyle \\begin{aligned} \\left(\\frac{4}{3}x^2+\\frac{3}{2}x\\right)^2 &amp; = \\left(\\frac{4}{3}x^2\\right)^2+2\\cdot \\frac{4}{3}x^2\\cdot \\frac{3}{2}x +\\left(\\frac{3}{2}x\\right)^2\\\\[2ex] &amp; = \\frac{4^2}{3^2}x^4+2\\cdot \\frac{12}{6}x^3 +\\frac{3^2}{2^2}x^2 \\\\[2ex] &amp;= \\frac{16}{9}x^4 +2\\cdot 2x^3+\\frac{9}{4}x^2 \\\\[2ex] &amp; = \\mathbf{\\frac{16}{9}} \\bm{x^4+4x^3+}\\mathbf{\\frac{9}{4}}\\bm{x^2}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"222\" width=\"416\" 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\u4e603<\/h3>\n<p>\u901a\u8fc7\u5e94\u7528\u603b\u548c\u5e73\u65b9\u516c\u5f0f\u8ba1\u7b97\u4ee5\u4e0b\u5e42\uff0c\u65e0\u9700\u4f7f\u7528\u8ba1\u7b97\u5668\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-86db45137cb4792d046d171c28662c90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"17^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"24\" style=\"vertical-align: 0px;\"><\/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\">\u9996\u5148\uff0c\u6570\u5b57\u5341\u4e03\u53ef\u4ee5\u5206\u89e3\u4e3a10\u52a07\u7684\u548c\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-55dc7f45d8d495163afd5d22d2c612ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"17^2=(10+7)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"117\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u6211\u4eec\u5c06\u529f\u7387\u8f6c\u6362\u4e3a\u5e73\u65b9\u548c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u73b0\u5728\u53ef\u4ee5\u5e94\u7528\u76f8\u5e94\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-83e35048f0ae6ae12bc2b5b3d761fb99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(10+7)^2 &amp; = 10^2+2\\cdot 10 \\cdot 7 +7^2 \\\\[2ex] &amp; =100+140+49\\\\[2ex] &amp; =289 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"100\" width=\"238\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7b80\u800c\u8a00\u4e4b\uff0c\u589e\u5f3a\u7684\u7ed3\u679c\u662f\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-d13bfdf83060795d27403604f251047d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"17^2=\\bm{289}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6b63\u5982\u60a8\u5728\u672c\u7ec3\u4e60\u4e2d\u770b\u5230\u7684\uff0c\u5e73\u65b9\u548c\u516c\u5f0f\u5bf9\u4e8e\u5728\u4e0d\u4f7f\u7528\u8ba1\u7b97\u5668\u7684\u60c5\u51b5\u4e0b\u8ba1\u7b97\u5927\u6570\u7684\u5e42\u4e5f\u5f88\u6709\u7528\u3002 <\/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=\"Cuadrado-de-una-suma-de-3-terminos\"><\/span>\u4e09\u9879\u4e4b\u548c\u7684\u5e73\u65b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6709\u65f6\u6211\u4eec\u53ef\u80fd\u4f1a\u53d1\u73b0\u6211\u4eec\u9700\u8981\u6c42\u89e3\u4e09\u4e2a\u76f8\u52a0\u9879\u7684\u5e73\u65b9\uff0c\u5373 (a+b+c) <sup>2<\/sup> \u3002\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u6211\u4eec\u4e0d\u80fd\u4f7f\u7528\u6211\u4eec\u89e3\u91ca\u7684\u516c\u5f0f\uff0c\u56e0\u4e3a\u62ec\u53f7\u5185\u6709\u4e00\u4e2a\u4e09\u9879\u5f0f\u800c\u4e0d\u662f\u4e8c\u9879\u5f0f\u3002\u56e0\u6b64\u6709\u5fc5\u8981\u4f7f\u7528\u4e0d\u540c\u7684\u516c\u5f0f\u3002<\/p>\n<p> <strong>3\u9879\u4e4b\u548c\u7684\u5e73\u65b9\u516c\u5f0f<\/strong>\u5982\u4e0b\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-547cbf526b192d07d188c703a68f12e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\definecolor{blauquadreejemplo}{HTML}{ff5733}  \\newtcbox{\\mymath}[1][]{%     nobeforeafter, math upper, tcbox raise base,     enhanced, colframe=blauquadreejemplo,      boxrule=1.2pt, boxsep=2.5mm,     #1} \\begin{empheq}[box={\\mymath[colback=white, shadow={2.5mm}{-2.5mm}{0mm}{blauquadreejemplo!20!white,} ]}]{equation*}     (a+b+c)^2 = a^2+2a(b+c)+b^2+2bc+c^2 \\end{empheq}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"294\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u8fd9\u4e2a\u516c\u5f0f\u662f\u5982\u4f55\u5e94\u7528\u7684\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-d0816bbe156553fc1ef5920ac2b2e09f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} (2x+3y+5)^2 &amp; = (2x)^2 + 2\\cdot 2x (3y+5)+(3y)^2+2\\cdot  3y \\cdot 5 + 5^2 \\\\[2ex] &amp; =4x^2 +4x (3y+5)+9y^2+30y +25 \\\\[2ex] &amp;=4x^2 +12xy+20x+9y^2+30y +25 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"481\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u5411\u516c\u5f0f\u4e2d\u6dfb\u52a0\u4e00\u4e2a\u5143\u7d20\u4f1a\u4f7f\u7ed3\u679c\u53d8\u5f97\u66f4\u52a0\u590d\u6742\u3002<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u603b\u548c\u5e73\u65b9\u7684\u516c\u5f0f\uff0c\u5373\u8457\u540d\u7684\u6052\u7b49\u5f0f (a+b) 2 \u3002\u60a8\u8fd8\u53ef\u4ee5\u770b\u5230\u5e73\u65b9\u548c\u7684\u793a\u4f8b\u548c\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%80%bb%e5%92%8c%e7%9a%84%e5%b9%b3%e6%96%b9%e6%88%96%e5%b9%b3%e6%96%b9%e5%92%8c\/\"> <span class=\"screen-reader-text\">\u603b\u548c\u7684\u5e73\u65b9\uff08\u6216\u5e73\u65b9\u548c\uff09<\/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-318","post","type-post","status-publish","format-standard","hentry","category-10"],"yoast_head":"<!-- This site is optimized 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