{"id":1249,"date":"2020-07-11T12:55:43","date_gmt":"2020-07-11T04:55:43","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1249"},"modified":"2024-06-29T07:33:29","modified_gmt":"2024-06-28T23:33:29","slug":"identities","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/identities\/","title":{"rendered":"2. \u6046\u7b49\u5f0f (Identities)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1249\" class=\"elementor elementor-1249\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fd720d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fd720d0\" 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-02bcf05\" data-id=\"02bcf05\" 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-edf2029 elementor-widget elementor-widget-text-editor\" data-id=\"edf2029\" 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>2.1\u00a0\u00a0 \u6052\u7b49\u5f0f\u7684\u7fa9\u610f<\/h2><p>\u6052\u7b49\u5f0f\u4fc2\u6307\u7b49\u865f\u5de6\u65b9\u8207\u53f3\u65b9\u7d93\u904b\u7b97\u5f8c\u6709\u5b8c\u5168\u76f8\u540c\u7684\u9805(terms)\u3002<\/p><p>\u70ba\u5497\u53ef\u5f37\u8abf\u300c\u6052\u7b49\u300d\uff0c\u6578\u5b78\u5bb6\u4f5c\u5497\u4e00\u500b&#8221;\u6052\u7b49&#8221;\u7b26\u865f \\(\\equiv\\)\u3002<\/p><p>\u4f8b\uff1a\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u8b49\u660e (<em>x<\/em> + 1) (<em>x<\/em> + 4) = (<em>x<\/em> + 2) (<em>x<\/em> + 3) &#8211; 2 \u662f\u6046\u7b49\u5f0f\u3002<br \/>\u89e3\uff1a<\/p><p style=\"padding-left: 80px;\">\\( \\begin{align}<br \/>\u5de6\u65b9 &amp; =\u3000(x + 1) (x + 4) \\\\<br \/>&amp; = \u3000x^{2} + x + 4x + 4 \\\\<br \/>&amp; = \u3000x^{2} + 5x + 4 \\\\<br \/>\u53f3\u65b9 &amp; =\u3000(x + 2) (x + 3)-2 \\\\<br \/>&amp; = \u3000x^{2} + 2x + 3x + 6-2 \\\\<br \/>&amp; = \u3000x^{2} + 5x + 4 \\\\<br \/>\\because \\quad &amp; \u5de6\u65b9\u3000=\u3000\u53f3\u65b9 \\\\<br \/>\\therefore \\quad &amp; (x + 1) (x + 4) \\equiv\u00a0 (x + 2) (x + 3)-2 <br \/>\\end{align} \\)<\/p><p>\u6b64\u5916\uff0c\u5c0d\u6046\u7b49\u5f0f\u4e2d\u7684\u8b8a\u6578x\u4ee3\u4e0a\u4efb\u610f\u6578\uff0c\u6046\u7b49\u5f0f\u4f9d\u7136\u6210\u7acb\u3002<\/p><p>\u4f8b\uff1a\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u82e5<em>A<\/em>(<em>x<\/em> + 2) &#8211; 4 \u2263 3(<em>x<\/em> + 1) &#8211; <em>B<\/em>\uff0c\u6c42<em>A<\/em>\u548c<em>B<\/em>\u7684\u503c\u3002<br \/>\u89e3\uff1a<\/p><p style=\"padding-left: 80px;\">\\(\\begin{align}<br \/>\u4ee3x = \uff0d2\uff0c \\quad \\quad \\\\<br \/>A(-2 + 2)-4 &amp; = 3(-2 + 1)-B \\\\<br \/>&#8211; 4 &amp; = -3-B \\\\<br \/>B &amp; = 1 \\\\<br \/>\u4ee3x = 0\uff0c\\quad \\quad \\quad \\\\<br \/>A(0 + 2)-4 &amp; = 3(0 + 1)-1 \\\\<br \/>2A-4 &amp; = 3-1 \\\\<br \/>2A &amp; = 6 \\\\<br \/>A &amp; = 3 \\\\<br \/>\\end{align} \\)<\/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-5f0a5d7 elementor-widget elementor-widget-text-editor\" data-id=\"5f0a5d7\" 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>2.2\u00a0\u00a0 \u5e38\u7528\u7684\u6046\u7b49\u5f0f (Common Identities)<\/h2><ol><li style=\"list-style-type: none;\"><ul><li>\u00a0\\((a + b) (a &#8211; b) = a^{2}-b^{2}\\)<\/li><li>\\( (a + b)^{2} = a^{2} + 2ab + b^{2} \\)<\/li><li>\\( (a-b)^{2} = a^{2}-2ab + b^{2} \\)<\/li><li>\\( a^{3} + b^{3} = (a + b)(a^{2}-ab + b^{2}) \\)<\/li><li>\\( a^{3}-b^{3} = (a-b)(a^{2} + ab + b^{2}) \\)<\/li><\/ul><\/li><\/ol><p>\u4f8b\uff1a\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u5c55\u958b (5 &#8211; 2<em>a<\/em>)<sup>2<br \/><\/sup>\u89e3\uff1a\u00a0\u00a0\u00a0<\/p><p style=\"padding-left: 40px;\">\\(\\begin{align}<br \/>(5-2a)^{2}\u00a0 &amp; = 5^{2}-2(5)(2a)+(2a)^{2} \\\\<br \/>&amp; = 25-20a+4a^{2}<br \/>\\end{align} \\)<\/p>\t\t\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-99fb40c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"99fb40c\" 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-1d06602\" data-id=\"1d06602\" 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-9712f6e elementor-widget elementor-widget-text-editor\" data-id=\"9712f6e\" 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<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/approximation-errors\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u8fd1\u4f3c\u8207\u8aa4\u5dee<\/a>\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-66a2d8b\" data-id=\"66a2d8b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\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-e97a733\" data-id=\"e97a733\" 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-1f6b57a elementor-widget elementor-widget-text-editor\" data-id=\"1f6b57a\" 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 style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/factorization\/\">\u56e0\u5f0f\u5206\u89e3 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/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\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-331d4ca\" data-id=\"331d4ca\" 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-87a77b9 elementor-widget elementor-widget-sidebar\" data-id=\"87a77b9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-3 > ul > li > a, .custom-menu-widget .ocean_custom_menu-3 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-3.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e8c\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-3 left dropdown-hover\"><ul id=\"menu-form2mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1248\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1248\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/approximation-errors\/\" class=\"menu-link\">1. \u8fd1\u4f3c\u8207\u8aa4\u5dee (Approximation &#038; Errors)<\/a><\/li>\n<li  id=\"menu-item-1261\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1261\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/identities\/\" class=\"menu-link\">2. \u6046\u7b49\u5f0f (Identities)<\/a><\/li>\n<li  id=\"menu-item-1266\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1266\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/factorization\/\" class=\"menu-link\">3. \u56e0\u5f0f\u5206\u89e3 (Factorization)<\/a><\/li>\n<li  id=\"menu-item-1265\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1265\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/formulae\/\" class=\"menu-link\">4. \u516c\u5f0f (Formulae)<\/a><\/li>\n<li  id=\"menu-item-1278\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1278\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/simultaneous-linear-equations\/\" class=\"menu-link\">5. \u806f\u7acb\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b (Simultaneous Linear Equations)<\/a><\/li>\n<li  id=\"menu-item-1279\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1279\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/rate-and-ratio\/\" class=\"menu-link\">6. \u7387\u53ca\u6bd4 (Rate and Ratio)<\/a><\/li>\n<li  id=\"menu-item-1280\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1280\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/use-of-percentage\/\" class=\"menu-link\">7. \u767e\u4efd\u6cd5 (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1302\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1302\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/geometry\/\" class=\"menu-link\">8. \u5e7e\u4f55\u5b9a\u7406 (Geometry)<\/a><\/li>\n<li  id=\"menu-item-1303\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1303\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/pythagoras-theorem\/\" class=\"menu-link\">9. \u7562\u6c0f\u5b9a\u7406 (Pythagoras\u2019 Theorem)<\/a><\/li>\n<li  id=\"menu-item-1304\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1304\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/trigonometric-ratios\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4 (Trigonometric Ratios)<\/a><\/li>\n<li  id=\"menu-item-1305\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1305\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/areas-and-volumes\/\" class=\"menu-link\">11. \u9762\u7a4d\u548c\u9ad4\u7a4d (Areas and Volumes)<\/a><\/li>\n<li  id=\"menu-item-1306\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1306\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/statistics\/\" class=\"menu-link\">12. \u7d71\u8a08 (Statistics)<\/a><\/li>\n<li  id=\"menu-item-16137\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16137\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\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\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2.1\u00a0\u00a0 \u6052\u7b49\u5f0f\u7684\u7fa9\u610f \u6052\u7b49\u5f0f\u4fc2\u6307\u7b49\u865f\u5de6\u65b9\u8207\u53f3\u65b9\u7d93\u904b\u7b97\u5f8c\u6709\u5b8c\u5168\u76f8\u540c\u7684\u9805(terms)\u3002 \u70ba\u5497\u53ef\u5f37\u8abf\u300c\u6052\u7b49\u300d\uff0c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1238,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"ocean_front_end_style_editor":"no","ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"0","ocean_second_sidebar":"0","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"0","ocean_custom_header_template":"0","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"0","ocean_menu_typo_font_family":"0","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"0","footnotes":""},"class_list":["post-1249","page","type-page","status-publish","hentry","entry"],"yoast_head":"<!-- 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