{"id":123,"date":"2023-07-16T19:31:53","date_gmt":"2023-07-16T19:31:53","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e5%8d%93%e8%b6%8a%e7%9a%84%e4%ba%a7%e5%93%81\/"},"modified":"2023-07-16T19:31:53","modified_gmt":"2023-07-16T19:31:53","slug":"%e5%8d%93%e8%b6%8a%e7%9a%84%e4%ba%a7%e5%93%81","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e5%8d%93%e8%b6%8a%e7%9a%84%e4%ba%a7%e5%93%81\/","title":{"rendered":"\u5353\u8d8a\u7684\u4ea7\u54c1"},"content":{"rendered":"<h2 class=\"wp-block-heading\" id=\"que-son-los-productos-notables-o-identidades-notables\"><span id=\"Que_son_los_productos_notables_o_identidades_notables\">\u4ec0\u4e48\u662f\u5353\u8d8a\u7684\u4ea7\u54c1\u6216\u5353\u8d8a\u7684\u8eab\u4efd\uff1f<\/span><\/h2>\n<p><strong>\u663e\u7740\u6052\u7b49\u5f0f<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u663e\u7740\u4e58\u79ef\u6216\u663e\u7740\u7b49\u5f0f<\/strong>\uff0c\u662f\u53ef\u4ee5\u66f4\u5feb\u5730\u6c42\u89e3<a href=\"https:\/\/mathority.org\/cn\/\u591a\u9879\u5f0f\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u591a\u9879\u5f0f<\/a>\u7684\u4e58\u79ef\u548c\u5546\u7684\u6570\u5b66\u8d44\u6e90\u3002\u6b63\u5982\u201c\u6052\u7b49\u201d\u4e00\u8bcd\u6240\u8868\u660e\u7684\u90a3\u6837\uff0c\u8fd9\u4e9b\u7b49\u5f0f\u4f7f\u6211\u4eec\u80fd\u591f\u8ba1\u7b97\u8fd9\u4e9b\u8fd0\u7b97\u800c\u65e0\u9700\u6c42\u89e3\u5b83\u4eec\u3002\u56e0\u4e3a\u6211\u4eec\u77e5\u9053\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u9075\u5faa\u56fa\u5b9a\u7684\u89c4\u5219\uff08\u603b\u662f\u6ee1\u8db3\u7684\uff09\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u7ed3\u679c\u800c\u4e0d\u5fc5\u68c0\u67e5\u5b83\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"cuando-usar-una-identidad-notable\">\u4f55\u65f6\u4f7f\u7528\u663e\u7740\u8eab\u4efd\uff1f<\/h3>\n<p>\u8fd9\u4e9b\u6052\u7b49\u5f0f\u4e3b\u8981\u7528\u5728\u4ee3\u6570\u9886\u57df\uff0c\u5b83\u4eec\u7684\u4e3b\u8981\u529f\u80fd\u662f\u52a0\u901f\u67d0\u4e2a\u591a\u9879\u5f0f\u7684\u6c42\u89e3\uff0c\u800c\u4e0d\u5fc5\u6c42\u89e3\u6574\u4e2a\u8fd0\u7b97\u672c\u8eab\u3002\u4ece\u90a3\u91cc\uff0c\u6211\u4eec\u83b7\u5f97\u4e86\u8457\u540d\u4ea7\u54c1\u7684\u914d\u65b9\uff0c\u6211\u4eec\u5c06\u5728\u6574\u7bc7\u6587\u7ae0\u4e2d\u5bf9\u5176\u8fdb\u884c\u8bc4\u8bba\u3002\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5<strong>\u5c06\u516c\u5f0f\u5e94\u7528\u4e8e<\/strong>\u5b8c\u6574\u5e73\u65b9\u3001<a href=\"https:\/\/mathority.org\/cn\/\u9636\u4e58\u591a\u9879\u5f0f\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u56e0\u5b50\u591a\u9879\u5f0f<\/a>\u6216\u4efb\u4f55\u5176\u4ed6\u7c7b\u578b\u7684\u8ba1\u7b97\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"como-resolver-un-producto-notable-paso-a-paso\">\u5982\u4f55\u4e00\u6b65\u6b65\u89e3\u51b3\u51fa\u4e00\u6b3e\u5353\u8d8a\u7684\u4ea7\u54c1\uff1f<\/h3>\n<p>\u4e3a\u4e86\u89e3\u6790\u663e\u7740\u7684\u8eab\u4efd\uff0c\u60a8\u9700\u8981\u9075\u5faa\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u8fc7\u7a0b\uff0c\u8fd9\u4e5f\u5f88\u6709\u610f\u4e49\uff1a<\/p>\n<ul>\n<li><strong>\u8bc6\u522b\u663e\u7740\u8eab\u4efd\u7684\u7c7b\u578b\uff1a<\/strong>\u7b2c\u4e00\u6b65\u662f\u8bc6\u522b\u64cd\u4f5c\u7684\u7c7b\u578b\uff1a\u663e\u7740\u4ea7\u54c1\u6216\u663e\u7740\u5546\u3002\u60a8\u8fd8\u5e94\u8be5\u6f84\u6e05\u60a8\u9700\u8981\u5e94\u7528\u4ec0\u4e48\u7c7b\u578b\u7684\u516c\u5f0f\uff0c\u5c3d\u7ba1\u7a0d\u540e\u6211\u4eec\u89e3\u91ca\u4e86\u4e0d\u540c\u7c7b\u578b\u7684\u663e\u7740\u6052\u7b49\u5f0f\u540e\u60a8\u5c31\u4f1a\u7406\u89e3\u8fd9\u4e00\u70b9\u3002<\/li>\n<li><strong>\u5e94\u7528\u516c\u5f0f\uff1a<\/strong>\u4e00\u65e6\u77e5\u9053\u9700\u8981\u5e94\u7528\u54ea\u4e2a\u516c\u5f0f\uff0c\u5c31\u53ef\u4ee5\u8fdb\u884c\u8ba1\u7b97\u4e86\u3002\u6839\u636e\u8eab\u4efd\u7684\u7c7b\u578b\uff0c\u60a8\u5c06\u5fc5\u987b\u89e3\u51b3\u6216\u591a\u6216\u5c11\u590d\u6742\u7684\u8fd0\u7b97\uff0c\u5e76\u4e14\u5728\u7edd\u5927\u591a\u6570\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e9b\u8ba1\u7b97\u5c06\u7531\u5305\u542b\u81f3\u5c11\u4e00\u4e2a\u672a\u77e5\u6570\u7684\u9879\u7ec4\u6210\u3002<\/li>\n<li><strong>\u7b80\u5316\u8868\u8fbe\u5f0f\uff1a<\/strong>\u6700\u540e\uff0c\u5f53\u5f97\u5230\u7ed3\u679c\u65f6\uff0c\u9700\u8981\u5bf9\u5176\u8fdb\u884c\u7b80\u5316\u3002\u5728\u6b64\u6b65\u9aa4\u4e2d\uff0c\u60a8\u9700\u8981\u5bf9\u76f8\u4f3c\u7684\u9879\u8fdb\u884c\u5206\u7ec4\u5e76\u5bf9\u5b83\u4eec\u8fdb\u884c\u6392\u5e8f\u4ee5\u5f62\u6210\u7ed3\u6784\u826f\u597d\u7684\u7ed3\u679c\u591a\u9879\u5f0f\u3002\u5e94\u8be5\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u4e00\u6b65\u4e0e\u5176\u4ed6\u6b65\u9aa4\u4e00\u6837\u91cd\u8981\uff0c\u5426\u5219\u7ec3\u4e60\u4ecd\u7136\u4e0d\u5b8c\u6574\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\" id=\"formulas-de-las-identidades-notables-o-productos-notables-principales\"><span id=\"Formulas_de_las_identidades_notables_o_productos_notables_principales\">\u663e\u7740\u8eab\u4efd\u6216\u4e3b\u8981\u663e\u7740\u4ea7\u54c1\u7684\u516c\u5f0f<\/span><\/h2>\n<p>\u60a8\u5c06\u5728\u4e0b\u9762\u627e\u5230\u4e0e\u8457\u540d\u6052\u7b49\u5f0f\u76f8\u5bf9\u5e94\u7684\u6240\u6709\u516c\u5f0f\u3002\u9664\u4e86\u6bcf\u4e2a\u6848\u4f8b\u7684\u7406\u8bba\u89e3\u91ca\u5916\uff0c\u8fd8\u6709\u4e00\u4e9b\u503c\u5f97\u6ce8\u610f\u7684\u5df2\u89e3\u51b3\u7684\u4ea7\u54c1\u793a\u4f8b\uff0c\u901a\u8fc7\u5b83\u4eec\u60a8\u5c06\u66f4\u597d\u5730\u7406\u89e3\u6240\u6709\u6982\u5ff5\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u5728\u7b2c\u4e00\u90e8\u5206\u4e2d\u60a8\u53ea\u4f1a\u627e\u5230<strong>\u6700\u91cd\u8981\u7684\u8eab\u4efd<\/strong>\u3002\u4f46\u662f\uff0c\u901a\u8fc7\u9605\u8bfb\u672c\u6587\uff0c\u60a8\u5c06\u5b66\u4e60\u5982\u4f55\u5f00\u53d1\u66f4\u590d\u6742\u7684\u8457\u540d\u4ea7\u54c1\uff0c\u4f8b\u5982\u7531\u4e09\u9879\u5f0f\u7ec4\u6210\u7684\u4ea7\u54c1\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"cuadrado-de-una-suma\">\u603b\u548c\u7684\u5e73\u65b9<\/h3>\n<p>\u7b2c\u4e00\u79cd\u60c5\u51b5\u6d89\u53ca\u548c<strong>\u7684\u5e73\u65b9<\/strong>\uff0c\u8fd9\u662f\u4ee3\u6570\u9886\u57df\u4e2d\u975e\u5e38\u5e38\u89c1\u7684\u591a\u9879\u5f0f\u8868\u8fbe\u5f0f\u3002\u8fd9\u53ef\u4ee5\u5199\u4e3a\uff1a (a + b) <sup>2<\/sup> \uff0c\u76f8\u5f53\u4e8e\uff1a (a + b) \u00b7 (a + b)\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u77e5\u9053\u53ef\u4ee5\u4f7f\u7528\u591a\u9879\u5f0f\u4e58\u6cd5\u6765\u6c42\u89e3\u3002\u4f46\u662f\uff0c\u7531\u4e8e\u663e\u7740\u7684\u6052\u7b49\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u6765\u8282\u7701\u65f6\u95f4\uff1a (a + b) <sup>2<\/sup> = a <sup>2<\/sup> + 2ab + b <sup>2<\/sup> \u3002\u63a5\u4e0b\u6765\u6211\u4eec\u7ed9\u5927\u5bb6<strong>\u6f14\u793a\u4e00\u4e0b\u521a\u624d\u770b\u5230\u7684\u516c\u5f0f<\/strong>\uff0c\u8fd9\u6837\u5927\u5bb6\u5c31\u80fd\u660e\u767d\u5b83\u7684\u51fa\u5904\u548c\u4f7f\u7528\u65b9\u6cd5\u4e86\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"317\" height=\"255\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-de-la-somme.webp\" data-src=\"\" alt=\"\u603b\u548c\u7684\u5e73\u65b9\" class=\"wp-image-7230 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u6211\u4eec\u6240\u770b\u5230\u7684\uff0c\u6211\u4eec\u4f7f\u7528\u4e4b\u524d\u8bc4\u8bba\u8fc7\u7684\u591a\u9879\u5f0f\u4e58\u6cd5\u8fdb\u884c\u4e86\u9a8c\u8bc1\u3002\u6211\u4eec\u53ef\u4ee5\u7edd\u5bf9\u80af\u5b9a\u5730\u8bf4\uff0c\u5982\u679c\u60a8\u719f\u8bb0\u7ed3\u679c\u516c\u5f0f\uff0c\u90a3\u4e48\u901a\u8fc7\u6267\u884c\u7b80\u5355\u7684<strong>\u503c\u66ff\u6362<\/strong>\uff0c\u60a8\u53ef\u4ee5\u66f4\u5feb\u5730\u5f97\u5230\u7ed3\u679c\u3002\u6240\u4ee5\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u7528\u7684\u6570\u5b66\u6982\u5ff5\u3002\u73b0\u5728\u60a8\u5df2\u7ecf\u4e86\u89e3\u4e86\u603b\u548c\u7684\u5e73\u65b9\u662f\u5982\u4f55\u8ba1\u7b97\u7684\uff0c\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u4e00\u4e2a\u5177\u4f53\u7684\u793a\u4f8b\uff1a<\/p>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-del-cuadrado-de-una-suma\">\u603b\u548c\u7684\u5e73\u65b9\u793a\u4f8b<\/h4>\n<p><strong>\u8ba1\u7b97\u663e\u7740\u6052\u7b49\u5f0f (2x + 4) <sup>2<\/sup> \uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"369\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-du-carre-dune-somme-resolue.webp\" data-src=\"\" alt=\"\u6c42\u548c\u7684\u5e73\u65b9\u7684\u793a\u4f8b\" class=\"wp-image-7231 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u57fa\u672c\u4e0a\uff0c\u6211\u4eec\u5c06\u4e8c\u9879\u5f0f\u7684\u503c\u4e0e\u516c\u5f0f\u7684\u5b57\u6bcd\u76f8\u5173\u8054\uff0c\u5e76\u6c42\u89e3\uff1aa = 2x \u548c b = 4\u3002\u6700\u540e\uff0c\u5728\u6c42\u89e3\u5b8c\u6240\u6709\u8ba1\u7b97\u540e\uff0c\u6211\u4eec\u5f97\u5230\u591a\u9879\u5f0f 4x <sup>2<\/sup> + 16x + 16\uff0c\u5373<strong>\u76f8\u5f53\u4e8e\u539f\u6765\u7684<\/strong>.\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u4ece\u7b80\u5316\u591a\u9879\u5f0f\u83b7\u5f97\u4e86\u6269\u5c55\u591a\u9879\u5f0f\uff08\u6807\u51c6\u5f62\u5f0f\uff09\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"cuadrado-de-una-resta\">\u51cf\u6cd5\u7684\u5e73\u65b9<\/h3>\n<p>\u53e6\u4e00\u4e2a\u975e\u5e38\u5e38\u89c1\u7684\u8868\u8fbe\u5f0f\u662f<strong>\u51cf\u6cd5\u7684\u5e73\u65b9<\/strong>\uff0c\u5b83\u5f88\u50cf\u52a0\u6cd5\u7684\u5e73\u65b9\uff0c\u53ea\u662f\u6539\u53d8\u4e86\u4e00\u4e2a\u7b26\u53f7\u3002\u90a3\u4e48\uff0c\u4e8c\u9879\u5f0f\u7684\u7ed3\u6784\u5c31\u7b49\u4ef7\u4e8e\uff1a (a \u2013 b) <sup>2<\/sup> \uff0c\u5982\u679c\u6211\u4eec\u5c55\u5f00\u5b83\uff0c\u6211\u4eec\u5f97\u5230\uff1a (a \u2013 b) \u00b7 (a \u2013 b)\u3002\u4e0e\u524d\u9762\u7684\u60c5\u51b5\u4e00\u6837\uff0c\u8fd9\u53ef\u4ee5\u901a\u8fc7\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\u6765\u8ba1\u7b97\uff0c\u5c3d\u7ba1\u5b83\u8fd8\u6709\u4e00\u4e2a\u6709\u52a9\u4e8e\u89e3\u51b3\u95ee\u9898\u7684\u516c\u5f0f\uff1aa <sup>2<\/sup> \u2013 2ab +b <sup>2<\/sup> \u3002\u60a8\u53ef\u4ee5\u5728\u4e0b\u9762\u627e\u5230\u8fd9\u65b9\u9762\u7684\u7ecf\u9a8c\u8bc1\u660e\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"317\" height=\"260\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-dune-soustraction.webp\" data-src=\"\" alt=\"\u51cf\u6cd5\u7684\u5e73\u65b9\" class=\"wp-image-7233 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4e3a\u4e86\u7b80\u5316\u6c42\u5dee\u5e73\u65b9\u7684\u8fc7\u7a0b\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e0e\u5e73\u65b9\u548c\u76f8\u540c\u7684\u516c\u5f0f\uff0c\u4f46\u7b2c\u4e00\u4e2a<strong>\u7b26\u53f7\u4e3a\u8d1f<\/strong>\u3002\u8fd9\u79cd\u6700\u5c0f\u7684\u53d8\u5316\u5141\u8bb8\u8868\u8fbe\u5f0f\u9002\u5e94\u7531\u6b63\u9879\u548c\u8d1f\u9879\u7ec4\u6210\u7684\u4e8c\u9879\u5f0f\uff0c\u8fd9\u5bf9\u4e8e\u51cf\u6cd5\u5f88\u6709\u7528\u3002\u73b0\u5728\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u4e00\u4e2a\u5df2\u89e3\u51b3\u7684\u793a\u4f8b\uff1a<\/p>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-del-cuadrado-de-una-resta\">\u51cf\u6cd5\u7684\u5e73\u65b9\u793a\u4f8b<\/h4>\n<p><strong>\u8ba1\u7b97\u663e\u7740\u6052\u7b49\u5f0f (x \u2013 3) <sup>2<\/sup> \uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"289\" height=\"269\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-du-carre-dune-soustraction-resolue.webp\" data-src=\"\" alt=\"\u6c42\u89e3\u51cf\u6cd5\u5e73\u65b9\u7684\u793a\u4f8b\" class=\"wp-image-7234 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u6b63\u5982\u60a8\u5728\u793a\u4f8b\u89e3\u51b3\u65b9\u6848\u4e2d\u770b\u5230\u7684\uff0c\u6211\u4eec\u5c06\u4e8c\u9879\u5f0f\u7684\u503c\u4ee3\u5165\u516c\u5f0f\u4e2d\uff0ca = x \u548c b = 3\u3002\u56e0\u6b64\uff0c\u4f7f\u7528\u6211\u4eec\u4e4b\u524d\u89e3\u91ca\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u53ea\u9700\u8981\u8fdb\u884c\u66ff\u6362\u548c\u4e00\u4e9b\u975e\u5e38\u57fa\u672c\u7684\u64cd\u4f5c\u8ba1\u7b97\u3002\u8fd9\u4f7f\u6211\u4eec\u80fd\u591f\u770b\u5230\u4f7f\u7528\u8be5\u8868\u8fbe\u5f0f\u8ba1\u7b97\u5dee\u503c\u7684\u5e73\u65b9\u662f\u591a\u4e48\u5bb9\u6613\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"diferencia-de-cuadrados-o-suma-por-diferencia\">\u5e73\u65b9\u5dee\u6216\u5dee\u4e4b\u548c<\/h3>\n<p>\u663e\u7740\u4e58\u79ef\u7684\u7b2c\u4e09\u79cd\u60c5\u51b5\u79f0\u4e3a<strong>\u5e73\u65b9\u5dee<\/strong>\uff0c\u5b83\u7531\u6b63\u4e8c\u9879\u5f0f\u548c\u8d1f\u4e8c\u9879\u5f0f\u7684\u4e58\u79ef\u5f62\u6210\u3002\u8fd9\u79cd\u98ce\u683c\u7684\u8868\u8fbe\u5f0f\u5177\u6709\u4ee5\u4e0b\u7ed3\u6784\uff1a (a + b) \u00b7 (a \u2013 b)\uff0c\u56e0\u6b64\u5982\u679c\u6211\u4eec\u5c55\u5f00\u8be5\u4e58\u79ef\uff0c\u6211\u4eec\u5c06\u5f97\u5230\u4f7f\u8ba1\u7b97\u66f4\u5bb9\u6613\u7684\u516c\u5f0f\uff1aa <sup>2<\/sup> \u2013 b <sup>2<\/sup> \u3002\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u516c\u5f0f\uff0c\u5c3d\u7ba1\u8981\u5b8c\u5168\u7406\u89e3\u5b83\uff0c\u60a8\u9700\u8981\u8fdb\u884c\u6240\u6709\u8ba1\u7b97\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"233\" height=\"182\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/somme-par-difference.webp\" data-src=\"\" alt=\"\u5dee\u548c\" class=\"wp-image-7235 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-de-la-suma-por-diferencia\">\u6c42\u548c\u9664\u4ee5\u5dee\u7684\u793a\u4f8b<\/h4>\n<p><strong>\u8ba1\u7b97\u663e\u7740\u6052\u7b49\u5f0f (x + 1) \u00b7 (x \u2013 4)\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"252\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-somme-par-difference.webp\" data-src=\"\" alt=\"\u6c42\u548c\u9664\u4ee5\u5dee\u7684\u793a\u4f8b\" class=\"wp-image-7236 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u8fd9\u6b21\u7684\u6570\u503c\u8ba1\u7b97\u975e\u5e38\u7b80\u5355\uff0c\u5b9e\u9645\u4e0a\u6211\u4eec\u53ea\u9700\u8981\u6c42\u89e3\u5e42\u5373\u53ef\u3002\u5c3d\u7ba1\u8be5\u516c\u5f0f\u786e\u5b9e<strong>\u4ec5\u9002\u7528\u4e8e<\/strong>\u4e8c\u9879\u5f0f\u5177\u6709\u76f8\u540c\u7684\u4e3b\u9879\u548c\u76f8\u540c\u7684\u72ec\u7acb\u9879\u4f46\u7b26\u53f7\u53d1\u751f\u53d8\u5316\u7684\u60c5\u51b5\u3002\u56e0\u6b64\uff0c\u8fd9\u4e00\u8eab\u4efd\u5f88\u91cd\u8981\uff0c\u4f46\u5b83\u4e0d\u662f\u60a8\u6700\u5e38\u4f7f\u7528\u7684\u8eab\u4efd\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"producto-de-dos-binomios-con-termino-comun\">\u5177\u6709\u5171\u540c\u9879\u7684\u4e24\u4e2a\u4e8c\u9879\u5f0f\u7684\u4e58\u79ef<\/h3>\n<p>\u5728\u7b2c\u56db\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u53d1\u73b0\u81ea\u5df1\u9762\u4e34\u7684\u60c5\u51b5\u4e0e\u524d\u4e00\u79cd\u60c5\u51b5\u975e\u5e38\u76f8\u4f3c\uff0c\u5c3d\u7ba1\u7ed3\u6784\u7565\u6709\u4fee\u6539\u3002\u89c2\u5bdf\u6211\u4eec\u5411\u60a8\u5c55\u793a\u7684\u5dee\u5f02\uff1a(x + a) \u00b7 (x + b) \u548c (a + b) \u00b7 (a \u2013 b)\u3002\u5982\u679c\u60a8\u4ecd\u7136\u4e0d\u592a\u6e05\u695a\uff0c\u8bf7\u8003\u8651\u4ee5\u4e0b\u793a\u4f8b\uff1a(x + 4) \u00b7 (x + 5) \u548c (x + 4) \u00b7 (x \u2013 4)\u3002\u5728\u7b2c\u4e00\u79cd\u60c5\u51b5\uff08<strong>\u4e24\u4e2a\u516c\u5171\u9879\u4e8c\u9879\u5f0f\u7684\u4e58\u79ef<\/strong>\uff09\u4e2d\uff0c\u53ea\u6709\u4e00\u4e2a\u5171\u4eab\u9879\uff0c\u800c\u5728\u7b2c\u4e8c\u79cd\u60c5\u51b5\uff08\u5dee\u4e4b\u548c\uff09\u4e2d\uff0c\u8fd9\u4e24\u4e2a\u9879\u662f\u516c\u5171\u9879\uff0c\u4f46\u72ec\u7acb\u9879\u6709\u5012\u53f7\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ec0\u4e48\u516c\u5f0f\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"140\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-de-binomes-avec-terme-commun.webp\" data-src=\"\" alt=\"\u4e8c\u9879\u5f0f\u4e0e\u516c\u5171\u9879\u7684\u4e58\u79ef\" class=\"wp-image-7259 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-del-producto-de-dos-binomios-con-termino-comun\">\u5177\u6709\u5171\u540c\u9879\u7684\u4e24\u4e2a\u4e8c\u9879\u5f0f\u7684\u4e58\u79ef\u793a\u4f8b<\/h4>\n<p><strong>\u6c42\u89e3\u663e\u7740\u4e58\u79ef (x + 2) \u00b7 (x + 3)\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"235\" height=\"237\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-produit-de-binomes-avec-un-terme-commun.webp\" data-src=\"\" alt=\"\u4e8c\u9879\u5f0f\u4e0e\u516c\u5171\u9879\u7684\u4e58\u79ef\u793a\u4f8b\" class=\"wp-image-7260 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4f7f\u7528 x <sup>2<\/sup> + (a + b)x + ab \u7684\u516c\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u4e24\u4e2a\u4e8c\u9879\u5f0f\u76f8\u4e58<strong>\u5f97\u5230\u7684\u4e8c\u6b21\u591a\u9879\u5f0f<\/strong>\u3002\u6211\u4eec\u5e0c\u671b\u901a\u8fc7\u8fd9\u4e2a\u4f8b\u5b50\u60a8\u5df2\u7ecf\u7406\u89e3\u4e86\u6211\u4eec\u89e3\u91ca\u7684\u6700\u540e\u4e24\u79cd\u60c5\u51b5\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u56e0\u4e3a\u6709\u65f6\u5f88\u96be\u533a\u5206\u5b83\u4eec\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"cuadrado-de-un-trinomio\">\u4e09\u9879\u5f0f\u7684\u5e73\u65b9<\/h3>\n<p>\u5f53\u6211\u4eec\u5c1d\u8bd5\u8ba1\u7b97<strong>\u4e09\u9879\u5f0f\u7684\u5e73\u65b9\u65f6\uff0c<\/strong>\u6211\u4eec\u8fd8\u6709\u4e00\u4e2a\u51fa\u8272\u7684\u4ea7\u54c1\u53ef\u4ee5\u8ba9\u6211\u4eec\u7684\u751f\u6d3b\u53d8\u5f97\u66f4\u8f7b\u677e\u3002\u8be5\u8868\u8fbe\u5f0f\u8868\u793a\u5982\u4e0b\uff1a(a + b + c) <sup>2<\/sup> \uff0c\u7b49\u6548\u4e58\u79ef\u4e3a\uff1aa <sup>2<\/sup> + b <sup>2<\/sup> + c <sup>2<\/sup> + 2ab + 2ac + 2bc\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u5728\u6b63\u4e09\u9879\u5f0f\u7684\u60c5\u51b5\u4e0b\u6709\u6548\uff0c\u4f46\u5982\u679c\u5176\u4e2d\u4e00\u4e2a\u7cfb\u6570\u4e3a\u8d1f\uff0c\u5219\u53ea\u9700\u5c06\u8d1f\u503c\u5199\u5165\u516c\u5f0f\u5373\u53ef\u3002\u4e0b\u9762\u662f\u516c\u5f0f\u7684\u6f14\u793a\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"460\" height=\"233\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/carre-dun-trinome.webp\" data-src=\"\" alt=\"\u4e09\u9879\u5f0f\u7684\u5e73\u65b9\" class=\"wp-image-7265 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-del-cuadrado-de-un-trinomio\">\u4e09\u9879\u5f0f\u7684\u5e73\u65b9\u793a\u4f8b<\/h4>\n<p><strong>\u8ba1\u7b97\u663e\u7740\u6052\u7b49\u5f0f (2x + 1 + x <sup>2<\/sup> ) <sup>2<\/sup> \uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"288\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-du-carre-dun-trinome.webp\" data-src=\"\" alt=\"\u4e09\u9879\u5f0f\u7684\u5e73\u65b9\u793a\u4f8b\" class=\"wp-image-7266 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Ejemplo-del-cuadrado-de-un-trinomio.png 548w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Ejemplo-del-cuadrado-de-un-trinomio-500x263.png 500w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\" id=\"formulas-de-las-identidades-notables-o-productos-notables-al-cubo\"><span id=\"Formulas_de_las_identidades_notables_o_productos_notables_al_cubo\">\u5353\u8d8a\u7684\u8eab\u4efd\u516c\u5f0f\u6216\u5353\u8d8a\u7684\u7acb\u65b9\u4ea7\u54c1<\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u89e3\u91ca\u4e86\u4e3b\u8981\u7684\u503c\u5f97\u6ce8\u610f\u7684\u6052\u7b49\u5f0f\uff0c\u6211\u4eec\u5c06\u770b\u770b<strong>\u5b83\u4eec\u7684\u5bfc\u6570<\/strong>\uff0c\u4ece\u4e8c\u9879\u5f0f\u7684\u4e09\u6b21\u65b9\u5f00\u59cb\u3002\u4e3a\u4e86\u8ba1\u7b97\u8fd9\u79cd\u98ce\u683c\u7684\u8457\u540d\u4ea7\u54c1\uff0c\u6211\u4eec\u5c06\u4e0d\u5f97\u4e0d\u6c42\u52a9\u4e8e\u7a0d\u5fae\u590d\u6742\u4e00\u70b9\u7684\u516c\u5f0f\uff0c\u4f46\u5176\u7ed3\u6784\u4e0e\u6211\u4eec\u5df2\u7ecf\u8ba8\u8bba\u8fc7\u7684\u7c7b\u4f3c\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"binomio-al-cubo\">\u4e8c\u9879\u5f0f\u7acb\u65b9<\/h3>\n<p><strong>\u4e8c\u9879\u5f0f\u7684\u7acb\u65b9<\/strong>\u5199\u4e3a\uff1a (a + b) <sup>3<\/sup>\u548c (a \u2013 b) <sup>3<\/sup> \uff0c\u8be5\u8868\u8fbe\u5f0f\u7b49\u4ef7\u4e8e\u4ee5\u4e0b\u516c\u5f0f\uff1a (a <sup>3<\/sup> + 3a <sup>2<\/sup> b + 3ab <sup>2<\/sup> + b <sup>3<\/sup> )\uff0c\u548c (a <sup>3<\/sup> \u2013 3a <sup>2<\/sup> b + 3ab <sup>2<\/sup> \u2013 b <sup>3<\/sup> )\u3002\u8fd9\u4e24\u79cd\u60c5\u51b5\u79f0\u4e3a\u548c\u7684\u7acb\u65b9\u548c\u51cf\u6cd5\u7684\u7acb\u65b9\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u7acb\u65b9\u4e8c\u9879\u5f0f\u3002\u4e0b\u9762\u60a8\u5c06\u770b\u5230\u6bcf\u4e2a\u6848\u4f8b\u7684\u975e\u5e38\u8be6\u7ec6\u7684\u6f14\u793a\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"555\" height=\"357\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cube-dune-somme-binomiale.webp\" data-src=\"\" alt=\"\u4e8c\u9879\u5f0f\u548c\u7684\u7acb\u65b9\" class=\"wp-image-7237 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-una-suma-de-binomio.png 555w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-una-suma-de-binomio-500x322.png 500w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"545\" height=\"366\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cube-dune-soustraction-binomiale.webp\" data-src=\"\" alt=\"\u4e8c\u9879\u5f0f\u51cf\u6cd5\u7684\u7acb\u65b9\" class=\"wp-image-7242 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-una-resta-de-binomio.png 545w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-una-resta-de-binomio-500x336.png 500w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<p>\u7406\u89e3\u7b2c\u4e00\u4e2a\u8bc1\u660e\u7684\u5173\u952e\u662f\u7406\u89e3 (a + b) <sup>3<\/sup>\u7b49\u4ef7\u4e8e\uff1a (a + b) <sup>2<\/sup> \u00b7 (a + b)\u3002\u8fd9\u6837\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u4f7f\u7528\u4e4b\u524d\u89e3\u91ca\u8fc7\u7684<strong>\u548c\u7684\u5e73\u65b9\u516c\u5f0f<\/strong>\u6765\u4e58\u4ee5\u53e6\u4e00\u4e2a\u56e0\u5b50\u3002\u7136\u540e\u6211\u4eec\u7b80\u5355\u5730\u7b80\u5316\u8868\u8fbe\u5f0f\uff0c\u5f97\u5230\u76f8\u5e94\u7684\u663e\u7740\u6052\u7b49\u5f0f\uff1aa <sup>3<\/sup> + 3a <sup>2<\/sup> b + 3ab <sup>2<\/sup> + b <sup>3<\/sup> \u3002\u5728\u7b2c\u4e8c\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u53d1\u751f\u4e86\u540c\u6837\u7684\u4e8b\u60c5\uff0c\u4f46\u7b26\u53f7\u53d1\u751f\u4e86\u53d8\u5316\u3002<\/p>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-del-cubo-de-un-binomio\">\u4e8c\u9879\u5f0f\u7acb\u65b9\u7684\u793a\u4f8b<\/h4>\n<p><strong>\u6c42\u89e3\u663e\u7740\u6052\u7b49\u5f0f (x + 3) <sup>3<\/sup> \uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"325\" height=\"263\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-du-cube-dune-somme.webp\" data-src=\"\" alt=\"\u603b\u548c\u7684\u7acb\u65b9\u793a\u4f8b\" class=\"wp-image-7241 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4f7f\u7528\u6211\u4eec\u521a\u521a\u8ba8\u8bba\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u591a\u9879\u5f0f\uff0c\u8003\u8651\u5230\uff1aa = xyb = 3\u3002\u5982\u60a8\u6240\u89c1\uff0c<strong>\u8fc7\u7a0b\u975e\u5e38\u7b80\u5355<\/strong>\uff0c\u8ba1\u7b97\u4e2d\u6ca1\u6709\u592a\u591a\u590d\u6742\u6027\uff0c\u56e0\u4e3a\u6211\u4eec\u6709\u516c\u5f0f\u3002\u5426\u5219\uff0c\u8981\u505a\u8fd9\u4e48\u591a\u4e58\u6cd5\u5c06\u662f\u76f8\u5f53\u4e4f\u5473\u7684\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"suma-de-cubos-y-diferencia-de-cubos\">\u7acb\u65b9\u548c\u4e0e\u7acb\u65b9\u5dee<\/h3>\n<p>\u6211\u4eec\u8fd8\u6709\u53e6\u4e00\u79cd\u60c5\u51b5\uff0c\u5b83\u5f88\u5bb9\u6613\u4e0e\u524d\u4e00\u79cd\u60c5\u51b5\u6df7\u6dc6\u3002\u867d\u7136\u4e24\u79cd\u60c5\u51b5\u5199\u6cd5\u4e0d\u540c\uff0c\u4f46\u5e76\u4e0d\u7b49\u540c\u3002\u76f8\u5f53\u4e8e<strong>\u7acb\u65b9\u4e4b\u548c\u6216\u5dee\u7684<\/strong>\u8868\u8fbe\u5f0f\u662f\uff1a a <sup>3<\/sup> + b <sup>3<\/sup> \uff0c\u800c\u5728\u524d\u9762\u7684\u4f8b\u5b50\u4e2d\u6211\u4eec\u8c08\u5230\uff1a (a + b) <sup>3<\/sup> \u3002\u6b63\u5982\u60a8\u6240\u770b\u5230\u7684\uff0c\u8868\u8fbe\u5f0f\u7684\u7ed3\u6784\u5b58\u5728\u4e0d\u53ef\u5426\u8ba4\u7684\u76f8\u4f3c\u6027\uff0c\u4f46\u5b9e\u9645\u4e0a\uff0c\u5728\u5c55\u5f00\u8ba1\u7b97\u65f6\uff0c\u5b83\u4eec\u662f\u4e24\u79cd\u5b8c\u5168\u4e0d\u540c\u7684\u60c5\u51b5\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"351\" height=\"110\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-pour-la-somme-des-cubes-et-la-difference-des-cubes.webp\" data-src=\"\" alt=\"\u7acb\u65b9\u548c\u4e0e\u7acb\u65b9\u5dee\u7684\u516c\u5f0f\" class=\"wp-image-7258 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5728\u516c\u5f0f\u7684\u6f14\u793a\u4e2d\uff0c\u6211\u4eec\u83b7\u5f97\u4e86<strong>\u7b2c\u4e00\u4e2a\u591a\u9879\u5f0f \u7684\u56e0\u5f0f\u5206\u89e3<\/strong>\uff0c\u51c6\u786e\u5730\u8bf4\uff0c\u6211\u4eec\u4ece\u521d\u59cb\u4e8c\u9879\u5f0f\u53d8\u4e3a\u4e8c\u9879\u5f0f\u4e0e\u4e09\u9879\u5f0f\u7684\u4e58\u79ef\u3002\u770b\u4f3c\u5f97\u5230\u7684\u7ed3\u679c (a + b) \u00b7 (a <sup>2<\/sup> \u2013 ab + b <sup>2<\/sup> ) \u5e76\u6ca1\u6709\u7b80\u5316\u8ba1\u7b97\uff0c\u4f46\u5b9e\u9645\u4e0a\uff0c\u901a\u8fc7\u5bf9\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u975e\u5e38\u5bb9\u6613\u7406\u89e3\u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-de-la-suma-de-cubos\">\u7acb\u65b9\u548c\u7684\u793a\u4f8b<\/h4>\n<p><strong>\u8ba1\u7b97\u663e\u7740\u4e58\u79ef x <sup>3<\/sup> + 27\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"227\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-somme-de-cubes.webp\" data-src=\"\" alt=\"\u7acb\u65b9\u548c\u7684\u793a\u4f8b\" class=\"wp-image-7256 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5f97\u5230\u7684\u7ed3\u679c\u76f8\u5f53\u957f\uff0c\u56e0\u4e3a\u5b83\u65e0\u6cd5\u8fdb\u4e00\u6b65\u7b80\u5316\u3002\u4f46\u662f\uff0c\u5f97\u5230\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u662f\u6b63\u5e38\u7684\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u60a8\u53ea\u80fd\u83b7\u5f97<strong>\u7ed3\u6784\u76f8\u5f53\u4e8e<\/strong>\u4e8c\u9879\u5f0f\u4e0e\u4e09\u9879\u5f0f\u4e58\u79ef\u7684\u7ed3\u679c\uff0c\u5982\u672c\u4f8b\u6240\u793a\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"trinomio-al-cubo\">\u4e09\u9879\u5f0f\u7684\u4e09\u6b21\u65b9<\/h3>\n<p><strong>\u4e09\u9879\u5f0f\u7684\u7acb\u65b9<\/strong>\u5199\u4e3a\uff1a (a + b + c) <sup>3<\/sup> \uff0c\u76f8\u5f53\u4e8e\u4e09\u4e2a\u76f8\u540c\u7684\u4e09\u9879\u5f0f\u76f8\u4e58\uff0c\u4f46\u6ca1\u6709\u6307\u6570\uff1a (a + b + c) \u00b7 (a + b + c) \u00b7 (a + b + c).\u5b83\u662f\u6700\u590d\u6742\u7684\u8457\u540d\u4ea7\u54c1\uff0c\u5c3d\u7ba1\u8be5\u516c\u5f0f\u975e\u5e38\u5408\u4e4e\u903b\u8f91\uff0c\u5e76\u4e14\u5728\u6267\u884c\u76f8\u5e94\u7684\u591a\u9879\u5f0f\u4e58\u6cd5\u65f6\u4ee5\u4e0e\u6240\u6709\u516c\u5f0f\u76f8\u540c\u7684\u65b9\u5f0f\u83b7\u5f97\u3002\u4e0b\u9762\u60a8\u5c06\u627e\u5230\u8fd9\u4e2a\u975e\u51e1\u6052\u7b49\u5f0f\u7684\u8bc1\u660e\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"877\" height=\"368\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/cube-dun-trinome.webp\" data-src=\"\" alt=\"\u4e09\u9879\u5f0f\u7684\u7acb\u65b9\" class=\"wp-image-7301 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-un-trinomio.png 877w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-un-trinomio-500x210.png 500w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-un-trinomio-800x336.png 800w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Cubo-de-un-trinomio-768x322.png 768w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<h4 class=\"wp-block-heading\" id=\"ejemplo-del-cubo-de-un-trinomio\">\u4e09\u9879\u5f0f\u7684\u7acb\u65b9\u793a\u4f8b<\/h4>\n<p><strong>\u6c42\u89e3\u4ee5\u4e0b\u4e09\u9879\u7acb\u65b9 (x <sup>2<\/sup> + 3x \u2013 4) <sup>3<\/sup> \uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"739\" height=\"432\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-travaille-du-cube-dun-trinome.webp\" data-src=\"\" alt=\"\u4e09\u9879\u5f0f\u7acb\u65b9\u7684\u4f8b\u5b50\" class=\"wp-image-7302 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Ejemplo-resuelto-del-cubo-de-un-trinomio.png 739w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Ejemplo-resuelto-del-cubo-de-un-trinomio-500x292.png 500w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\" id=\"cocientes-notables\"><span id=\"Cocientes_notables\">\u663e\u7740\u7684\u6bd4\u7387<\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u89e3\u91ca<strong>\u663e\u5546<\/strong>\uff0c\u5b83\u4eec\u662f\u5feb\u901f\u6c42\u89e3\u67d0\u4e9b\u7c7b\u578b\u4ee3\u6570\u5206\u6570\u7684\u663e\u7740\u6052\u7b49\u5f0f\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u6709\u56db\u79cd\u4e0d\u540c\u7684\u7c7b\u578b\uff0c\u5b83\u4eec\u6709\u4e00\u4e2a\u5171\u540c\u7684\u7279\u5f81\uff1a\u5b83\u4eec\u7684\u7ed3\u679c\u7531\u7cbe\u786e\u7684\u591a\u9879\u5f0f\u7ec4\u6210\uff08\u4f59\u6570\u4e3a\u96f6\uff09\u3002\u8fd8\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u5353\u8d8a\u5546\u7684\u516c\u5f0f\u4e0e\u6211\u4eec\u5df2\u7ecf\u89e3\u91ca\u8fc7\u7684\u5353\u8d8a\u4e58\u79ef\u7684\u516c\u5f0f\u6709\u4e00\u5b9a\u7684\u5173\u7cfb\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"238\" height=\"311\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/des-ratios-remarquables.webp\" data-src=\"\" alt=\"\u663e\u7740\u7684\u6bd4\u7387\" class=\"wp-image-7495 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\" id=\"ejemplo-de-cocientes-notables-resueltos\">\u5df2\u89e3\u51b3\u7684\u663e\u7740\u6bd4\u7387\u793a\u4f8b<\/h3>\n<p><strong>\u8ba1\u7b97\u4ee5\u4e0b\u91cd\u8981\u6bd4\u7387\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"321\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemples-de-quotients-remarquables.webp\" data-src=\"\" alt=\"\u663e\u7740\u5546\u7684\u4f8b\u5b50\" class=\"wp-image-7268 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\" id=\"ejercicios-de-productos-notables-resueltos\"><span id=\"Ejercicios_de_productos_notables_resueltos\">\u89e3\u51b3\u4e86\u51fa\u8272\u7684\u4ea7\u54c1\u7ec3\u4e60<\/span><\/h2>\n<p>\u73b0\u5728\u60a8\u5df2\u7ecf\u77e5\u9053\u5982\u4f55\u89e3\u51b3\u4e0d\u540c\u7684\u663e\u7740\u95ee\u9898\uff0c\u662f\u65f6\u5019\u8fdb\u884c\u4e00\u4e9b\u7ec3\u4e60\u4e86\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u4e3a\u60a8\u63d0\u4f9b<strong>6 \u4e2a\u7ec3\u4e60<\/strong>\u6765\u5e94\u7528\u6240\u89e3\u91ca\u7684\u6240\u6709\u7406\u8bba\u3002\u6211\u4eec\u5411\u60a8\u5c55\u793a\u4e86\u4e3b\u8981\u663e\u7740\u8eab\u4efd\u7684\u8868\u683c\uff0c\u4ee5\u4fbf\u60a8\u5728\u89e3\u51b3\u6240\u6709\u7ec3\u4e60\u65f6\u53ef\u4ee5\u8f7b\u677e\u638c\u63e1\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"311\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produits-remarquables.webp\" data-src=\"\" alt=\"\u5353\u8d8a\u7684\u4ea7\u54c1\" class=\"wp-image-7275 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Productos-notables.png 723w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/02\/Productos-notables-500x215.png 500w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\" id=\"ejercicio-1\">\u7ec3\u4e601<\/h3>\n<p><strong>\u6c42\u89e3\u4e8c\u9879\u5f0f\u5e73\u65b9 (x \u2013 4) <sup>2<\/sup> \u3001 (x + 1) <sup>2<\/sup>\u548c (x \u2013 3) <sup>2<\/sup> \uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"180\" height=\"671\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-du-carre-binomial.webp\" data-src=\"\" alt=\"\u4e8c\u9879\u5f0f\u5e73\u65b9\u7ec3\u4e60\" class=\"wp-image-7487 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Ejercicios-de-cuadrado-de-binomio.png 180w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Ejercicios-de-cuadrado-de-binomio-134x500.png 134w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\" id=\"ejercicio-2\">\u7ec3\u4e602<\/h3>\n<p><strong>\u8ba1\u7b97\u5e73\u65b9 (x \u2013 1) \u00b7 (x + 1) \u548c (x + 3) \u00b7 (x \u2013 3) \u7684\u4e24\u4e2a\u5dee\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"163\" height=\"404\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-daddition-par-difference.webp\" data-src=\"\" alt=\"\u5dee\u5206\u52a0\u6cd5\u7ec3\u4e60\" class=\"wp-image-7489 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\" id=\"ejercicio-3\">\u7ec3\u4e603<\/h3>\n<p><strong>\u5f00\u53d1\u7acb\u65b9 (x \u2013 5) <sup>3<\/sup>\u548c (x + 8) <sup>3<\/sup>\u7684\u8457\u540d\u4ea7\u54c1\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"426\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-sur-les-cubes-binomiaux.webp\" data-src=\"\" alt=\"\u4e8c\u9879\u5f0f\u7acb\u65b9\u7684\u7ec3\u4e60\" class=\"wp-image-7490 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\" id=\"ejercicio-4\">\u7ec3\u4e604<\/h3>\n<p><strong>\u5f00\u53d1\u7531\u591a\u56e0\u5b50\u9879 (4x <sup>2<\/sup> + 5y) <sup>2<\/sup> \u3001(5x <sup>3<\/sup> + y <sup>2<\/sup> ) \u00b7 (5x <sup>3<\/sup> \u2013 y <sup>2<\/sup> ) \u548c (5xy <sup>2<\/sup> \u2013 2xy) <sup>2<\/sup>\u5f62\u6210\u7684\u663e\u7740\u6052\u7b49\u5f0f\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"327\" height=\"681\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/identites-notables-formees-par-divers-facteurs.webp\" data-src=\"\" alt=\"\u5404\u79cd\u56e0\u7d20\u5f62\u6210\u7684\u663e\u7740\u8eab\u4efd\" class=\"wp-image-7491 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Identidades-notables-formadas-por-varios-factores.png 327w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Identidades-notables-formadas-por-varios-factores-240x500.png 240w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\" id=\"ejercicio-5\">\u7ec3\u4e605<\/h3>\n<p><strong>\u8ba1\u7b97\u7531\u591a\u56e0\u5b50\u9879 (3x <sup>2<\/sup> + y) <sup>3<\/sup>\u548c (5y <sup>3<\/sup> \u2013 2x <sup>2<\/sup> ) <sup>3<\/sup>\u5f62\u6210\u7684\u663e\u7740\u4e09\u6b21\u4e58\u79ef\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"504\" height=\"460\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-sur-les-produits-remarquables-en-cube.webp\" data-src=\"\" alt=\"\u7acb\u65b9\u4f53\u4e2d\u5353\u8d8a\u4ea7\u54c1\u7684\u7ec3\u4e60\" class=\"wp-image-7492 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Ejercicios-de-productos-notables-al-cubo.png 504w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Ejercicios-de-productos-notables-al-cubo-500x456.png 500w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\" id=\"ejercicio-6\">\u7ec3\u4e606<\/h3>\n<p><strong>\u6c42\u89e3\u4e09\u9879\u5f0f (2x <sup>2<\/sup><\/strong> <strong>+ 3x + 5) <sup>2<\/sup>\u548c (3x <sup>2<\/sup> + 5x + 6) \u7684\u5e73\u65b9\uff1a<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"565\" height=\"539\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercices-sur-les-carres-des-trinomes.webp\" data-src=\"\" alt=\"\u4e09\u9879\u5f0f\u7684\u5e73\u65b9\u7ec3\u4e60\" class=\"wp-image-7493 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Ejercicios-de-cuadrados-de-trinomios.png 565w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Ejercicios-de-cuadrados-de-trinomios-500x477.png 500w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u4ec0\u4e48\u662f\u5353\u8d8a\u7684\u4ea7\u54c1\u6216\u5353\u8d8a\u7684\u8eab\u4efd\uff1f \u663e\u7740\u6052\u7b49\u5f0f\uff0c\u4e5f\u79f0\u4e3a\u663e\u7740\u4e58\u79ef\u6216\u663e\u7740\u7b49\u5f0f\uff0c\u662f\u53ef\u4ee5\u66f4\u5feb\u5730\u6c42\u89e3\u591a\u9879\u5f0f\u7684\u4e58\u79ef\u548c\u5546\u7684\u6570\u5b66\u8d44 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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