{"id":1833,"date":"2020-08-16T15:09:22","date_gmt":"2020-08-16T07:09:22","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1833"},"modified":"2020-11-02T17:47:10","modified_gmt":"2020-11-02T09:47:10","slug":"polynomials-multiplication","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/polynomials-multiplication\/","title":{"rendered":"2. \u591a\u9805\u5f0f > \u591a\u9805\u5f0f\u7684\u4e58\u6cd5"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1833\" class=\"elementor elementor-1833\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8e2dd38 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8e2dd38\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-79e8470\" data-id=\"79e8470\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-293e014 elementor-widget elementor-widget-text-editor\" data-id=\"293e014\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2 class=\"page-header-title clr\">2.3 \u591a\u9805\u5f0f\u7684\u4e58\u6cd5<\/h2><p>\u8981\u505a\u597d\u591a\u9805\u5f0f\u5605\u4e58\u6cd5\uff0c\u540c\u5b78\u8981\u8b58\u4ee5\u4e0b\u56db\u6a23\u5622\uff1a<\/p><ul><li>\u4e58\u6cd5\u5206\u914d\u6027\u8cea<\/li><li>\u6b63\u8ca0\u6578\u76f8\u4e58<\/li><li>\u57fa\u790e\u6307\u6578\u5b9a\u5f8b<\/li><li>\u591a\u9805\u5f0f\u5605\u52a0\u3001\u6e1b\u6cd5<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-84d7940 elementor-widget elementor-widget-text-editor\" data-id=\"84d7940\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>2.3.1.\u00a0 \u4e58\u6cd5\u5206\u914d\u6027\u8cea\uff08Distributive property of multiplication\uff09<\/h3><p>\u6211\u8ad7\u6709\u597d\u591a\u540c\u5b78\u90fd\u6703\u554f\u54a9\u4fc2\u201c\u4e58\u6cd5\u5206\u914d\u6027\u8cea\u201d\uff1f\uff1f<\/p><p>\u5927\u5bb6\u5514\u597d\u4ffe\u500b\u540d\u5687\u89aa\u2026\u2026 \u5176\u5be6\u5373\u4fc2\u300c\u62c6\u4e58\u6cd5\u5605\u62ec\u865f\u300d\u3002<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\( 3 \\times ( 4 + 5 ) = 3 \\times 4 + 3 \\times 5 \\)<\/li><\/ul><\/li><\/ul><p>\u4f8b1\uff1a \u00a0\u00a0 \\( 3 ( 5a + 6 ) = 15a + 18\u00a0 \\)<\/p><ul><li><span style=\"color: #ff0000;\">\u7559\u610f\u6578\u5b57\u9084\u6578\u5b57\u4e58<\/span>\uff0c\u5373 \\((3) \\times (5a) = (3 \\times 5)a = 15a \\)<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-25e65be elementor-widget elementor-widget-text-editor\" data-id=\"25e65be\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>2.3.2.\u00a0 \u6b63\u8ca0\u6578\u76f8\u4e58<\/h3><p>\u6211\u8ad7\u5514\u99db\u591a\u8b1b\uff0c\u5927\u5bb6\u90fd\u77e5<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\\(3 \\times 4 = 12 \\)<\/li><li>\\(3 \\times (-5) = -15\\)<\/li><li>\\((-4) \\times (-5) = 20\\)<\/li><li>\\((-5) \\times 2 = -10 \\)<\/li><\/ul><\/li><\/ul><p style=\"text-align: center;\"><span style=\"color: #ff0000;\">\u5fc3\u7b97\u5514\u597d\u5514\u7dca\u8981\uff0c\u7528\u8a08\u7b97\u6a5f\u7be4\u5f97\u5feb\u53c8\u6e96\u91cd\u7dca\u8981\uff01<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7beda06 elementor-widget elementor-widget-text-editor\" data-id=\"7beda06\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>2.3.3.\u00a0 \u57fa\u790e\u6307\u6578\u5b9a\u5f8b<\/h3><p>\u6307\u6578\u4fc2\u201c\\(x^{2}\\)\u201d\u88e1\u9762\u500b\u201c2\u201d\uff0c\u5373\u4fc2\u6211\u5730\u6210\u65e5\u8b1b\u5605\u201c\uff12\u6b21\u65b9\u201d\u3001\u201c\uff13\u6b21\u65b9\u201d\u7b49\u3002<\/p><p>\u5927\u5bb6\u8981\u8b58\u5605\u4fc2\uff1a<\/p><ul><li>\\(x \\times x = x^{2}\u00a0\u00a0 {\\color{Red} \\quad \\leftarrow\u00a0 \u5514\u8a72\u7559\u610f\u500b x \u540c \u201c\u4e58\u201d\u5605\u5beb\u6cd5 }\\)<\/li><li>\\(x \\times x^{2} = x^{3}\u00a0 \\)<\/li><li>\\(a \\times b = ab \\)<\/li><\/ul><p>\u4f8b2\uff1a \u4ee3\u7c21 \u00a0\u00a0\u00a0 \\( (3y) \u00a0(2y) \\)<br \/>\u89e3\uff1a\u3000\\( (3y)(2y) = 6y^{2} \\quad \\quad {\\color{Red} \\leftarrow \u7559\u610f\u6578\u5b57\u9084\u6578\u5b57\u4e58\uff0c\u82f1\u6587\u5b57\uff08\u5373\u8b8a\u6578\uff09\u9084\u82f1\u6587\u5b57\u4e58 } \\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3edbbe6 elementor-widget elementor-widget-text-editor\" data-id=\"3edbbe6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3>2.3.4.\u00a0 \u591a\u9805\u5f0f\u7684\u52a0\u3001\u6e1b\u6cd5<\/h3><p>\u5514\u8b58\u5605\u8a71\u53ef\u4ee5\u7747\u8fd4\u300c<a href=\"https:\/\/www.study-together.com\/edu\/dse%e6%95%b8%e5%ad%b8-%e5%bf%85%e4%bf%ae%e9%83%a8%e5%88%86-core\/%e5%94%94%e5%a5%bd%e4%bb%a5%e7%82%ba%e5%94%94%e9%a7%9b%e8%80%83%e8%aa%b2%e9%a1%8c\/%e5%a4%9a%e9%a0%85%e5%bc%8f-%e5%a4%9a%e9%a0%85%e5%bc%8f%e7%9a%84%e5%8a%a0%e3%80%81%e6%b8%9b%e6%b3%95\/\">2.2. \u591a\u9805\u5f0f\u7684\u52a0\u3001\u6e1b\u6cd5<\/a>\u300d\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1d42f78 elementor-widget elementor-widget-heading\" data-id=\"1d42f78\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">\u7df4\u529f\u6642\u9593<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e2bdbda elementor-widget elementor-widget-accordion\" data-id=\"e2bdbda\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2371\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2371\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Level 1<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2371\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2371\"><ul><li>\\(3 (5y + 6) = 15y + 18 \\)<\/li><li>\\((5y &#8211; 6)(4) = (5y)(4) &#8211; (6)(4) = 20y &#8211; 24 \\)<\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2372\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2372\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Level 2<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2372\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2372\"><ul><li>\\(-3 (5y &#8211; 4) = -15y + 12\\)<br \/><br \/><p>\u6709D\u66f8\u6703\u6559\u5927\u5bb6\uff1a<br \/>\\(\\begin{align}<br \/>-3 (5y \u2013 4) &amp; = (-3) (5y) \u2013 (-3) (4) \\\\<br \/>&amp; = -15y \u2013 (-12) \\\\<br \/>&amp; = -15y + 12<br \/>\\end{align}\u00a0 \\)<\/p><p>\u4f46\u6211\u5c31\u89ba\u5f97\u53ea\u8981\u719f\u5206\u914d\u6027\u8cea\uff0c<br \/>\u00a0\u7b2c\u4e00\u9805\u5373\u4fc2\u201c(-3) (5y) = -15y\u3002<br \/>\u00a0\u7b2c\u4e8c\u9805\u5373\u4fc2\u201c(-3) (-4) = +12\u201d\u3002<br \/>\u53c8\u5feb\u53c8\u6613\u8ddf\u3002<\/p><br \/><p>\u00a0<\/p><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2373\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-2373\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Level 3<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2373\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-2373\"><p>\u4f8b1\uff1a\u00a0 \u5c55\u958b\u00a0 \\(\u00a0 (3x + 1) (2x \u2013 5) \u00a0 {\\color{Red} \u5c07\u5169\u500b\u591a\u9805\u5f0f\u76f8\u4e58\u901a\u5e38\u53eb\u201c\u5c55\u958b\u201d }\\)<\/p><p>\u5148\u5c07\u5f8c\u9762\u62ec\u865f\u5165\u9762\u5605\u201c2x &#8211; 5\u201d\u7576\u6210\u4e00\u500b\u516c\u4ed4\uff0c\u5373<br \/>\\( \\quad (3x + 1) (2x \u2013 5) = (3x + 1) (\u0394) = 3x\u0394 + \u0394 \\)<\/p><p>\u6240\u4ee5\u689d\u6578\u4fc2\u5481\u505a\u5605\uff1a<br \/>\\( \\begin{align}<br \/>&amp; (3x + 1) (2x \u2013 5) \\\\<br \/>&amp; = 3x (2x \u2013 5) + (2x \u2013 5)\u00a0\u00a0\u00a0 \\quad {\\color{Red} \u201c+ 1 (2x \u2013 5)\u201d\u4e2d\u56051\u7fd2\u6163\u4e0d\u5beb } \\\\<br \/>&amp; = 6x^{2} \u2013 15x + 2x \u2013 5\u00a0\u00a0\u00a0\u00a0 \\quad {\\color{Red}\u5206\u914d\u6027\u8cea \u53ca \u62c6\u62ec\u865f} \\\\<br \/>&amp; = 6x^{2} \u2013 13x \u2013 5 \u00a0 \\quad {\\color{Red} \u9032\u4e00\u6b65\u5316\u7c21\u7b54\u6848}<br \/>\\end{align} \\)<\/p><p>\u4f8b2\uff1a \u5c55\u958b\u00a0 \\((3x \u2013 2) (-2x + 5) \\)<\/p><p>\\( \\begin{align}<br \/>&amp; (3x \u2013 2) (-2x + 5) \\\\<br \/>&amp; = (3x) (-2x + 5) \u2013 2(-2x + 5)\u00a0\u00a0\u00a0\u00a0 \\quad {\\color{Red} \u5206\u914d\u6027\u8cea\uff0c\u7e3d\u4e4b\u5c07\u5f8c\u9762\u500b\u62ec\u865f\u7576\u6210\u5716\u756b\uff0c\u6bcf\u6b21\u6210\u500b\u6284 } \\\\<br \/>&amp; = -6x^{2} + 15x + 4x \u2013 10\u00a0\u00a0\u00a0\u00a0 \\quad {\\color{Red} \u5206\u914d\u6027\u8cea\uff0c\u7559\u610f \u201c-2\u201d\u4e58\u201c-2x\u201d\uff1d +4x } \\\\<br \/>&amp; = -6x^{2} + 19x \u2013 10 \\\\<br \/>\\end{align} \\)<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-0bdd7a1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0bdd7a1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6a0e6b2\" data-id=\"6a0e6b2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0ac471d elementor-widget elementor-widget-text-editor\" data-id=\"0ac471d\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><a href=\"https:\/\/www.study-together.com\/edu\/dse-maths-core\/junior_summary\/polynomials-addition-substraction\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u591a\u9805\u5f0f\u7684\u52a0\u3001\u6e1b\u6cd5<\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-ab171ed\" data-id=\"ab171ed\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div 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