{"id":178,"date":"2022-04-13T10:14:47","date_gmt":"2022-04-13T10:14:47","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=178"},"modified":"2025-01-22T11:00:55","modified_gmt":"2025-01-22T11:00:55","slug":"i-6-factorise-quadratics-using-algebra-tiles","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/i-6-factorise-quadratics-using-algebra-tiles\/","title":{"rendered":"I.6 Factorise quadratics using algebra tiles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong> Factorise quadratics using algebra tiles<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Introduction to Quadratic Equations:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Quadratic equations are second-degree polynomial equations in the form ax\u00b2 + bx + c = 0.<\/li>\n\n\n\n<li>They can be solved using various methods, and one approach is factorization.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Understanding Algebra Tiles:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Algebra tiles are physical or virtual manipulatives used to visualize algebraic expressions and equations.<\/li>\n\n\n\n<li>In the context of factorizing quadratics, we use algebra tiles to represent the quadratic expression in a visual way.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Representation of Quadratics with Algebra Tiles:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Square tiles represent the area model for the quadratic expression.<\/li>\n\n\n\n<li>Rectangle tiles represent the linear term.<\/li>\n\n\n\n<li>Unit tiles represent the constant term.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Factorization Process:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Arrange the tiles to form a rectangle (representing the quadratic expression).<\/li>\n\n\n\n<li>Look for ways to break down the rectangle into two smaller rectangles, each representing a linear expression.<\/li>\n\n\n\n<li>The side lengths of the rectangles will correspond to the factors of the quadratic expression.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Example: Factorizing x\u00b2 + 5x + 6:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Represent x\u00b2 + 5x + 6 using algebra tiles.<\/li>\n\n\n\n<li>Arrange the tiles to form a rectangle.<\/li>\n\n\n\n<li>Find dimensions that allow you to factor the quadratic expression.<\/li>\n\n\n\n<li>Write the factored form as (x + m)(x + n), where m and n are the dimensions.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Special Cases: Perfect Square Trinomials:<\/strong>\n<ul class=\"wp-block-list\">\n<li>If the quadratic expression is a perfect square trinomial, it can be factored into the square of a binomial.<\/li>\n\n\n\n<li>Example: \ufffd2+6\ufffd+9<em>x<\/em>2+6<em>x<\/em>+9 can be factored as (\ufffd+3)2(<em>x<\/em>+3)2.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Practice and Application:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Practice using algebra tiles for various quadratic expressions.<\/li>\n\n\n\n<li>Apply the factoring technique to solve quadratic equations.<\/li>\n\n\n\n<li>Verify solutions by multiplying the factors.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>General Formulas for Quadratic Factorization:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Factorizing \ufffd\ufffd2+\ufffd\ufffd+\ufffd<em>a<\/em><em>x<\/em>2+<em>b<\/em><em>x<\/em>+<em>c<\/em> involves finding two numbers whose product is ac and whose sum is b.<\/li>\n\n\n\n<li>The factored form is then (\ufffd\ufffd+\ufffd)(\ufffd\ufffd+\ufffd)(mx+p)(nx+q), where m, n, p, and q are the constants.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Review and Homework:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Review the process of factorization using algebra tiles.<\/li>\n\n\n\n<li>Assign homework exercises to reinforce the concept.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9ae5ed\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-f23d04292e315a112222ca411402fbc4\" style=\"color:#b00012\">Which&nbsp;area model represents the factorization&nbsp;<\/p>\n\n\n\n<p>3x<sup>2<\/sup>+12x+9=(x+3)(3x+3)?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design.png\" alt=\"\" class=\"wp-image-3733\" style=\"width:351px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1.png\" alt=\"\" class=\"wp-image-3734\" style=\"width:338px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-1.png\" alt=\"\" class=\"wp-image-3735\" style=\"width:262px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2.png\" alt=\"\" class=\"wp-image-3736\" style=\"width:278px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;area model represents the factorization&nbsp;3x<sup>2<\/sup>+12x+9=(x+3)(3x+3).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview.png\" alt=\"\" class=\"wp-image-3737\" style=\"width:312px;height:312px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;left side of the equation represents the total area written as the sum of all the tiles. There are&nbsp;3&nbsp;<em><span style=\"text-decoration: underline;\">x<\/span><\/em><sup><span style=\"text-decoration: underline;\">2<\/span><\/sup>&nbsp;tiles,&nbsp;12&nbsp;<em><span style=\"text-decoration: underline;\">x<\/span><\/em>&nbsp;tiles, and&nbsp;9&nbsp;<span style=\"text-decoration: underline;\">1<\/span>&nbsp;tiles, so the sum is&nbsp;3x<sup>2<\/sup>+12x+9.<\/p>\n\n\n\n<p>The&nbsp;right side of the equation represents the total area written as base times height. The base is made up of&nbsp;1&nbsp;<em><span style=\"text-decoration: underline;\">x<\/span><\/em>&nbsp;tile and&nbsp;3&nbsp;<span style=\"text-decoration: underline;\">1<\/span>&nbsp;tiles, so it is&nbsp;(x+3).&nbsp;The height is made up of&nbsp;3&nbsp;<em><span style=\"text-decoration: underline;\">x<\/span><\/em>&nbsp;tiles and&nbsp;3&nbsp;<span style=\"text-decoration: underline;\">1<\/span>&nbsp;tiles, so it is&nbsp;(3x+3).&nbsp;The base times the height is&nbsp;(x+3)(3x+3).<\/p>\n\n\n\n<p>The&nbsp;other area models represent factorizations of different&nbsp;polynomials.<\/p>\n\n\n\n<p>This&nbsp;area model shows&nbsp;3x<sup>2<\/sup>+11x+6=(x+3)(3x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview.png\" alt=\"\" class=\"wp-image-3738\" style=\"width:309px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;2x<sup>2<\/sup>+8x+6=(x+3)(2x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview.png\" alt=\"\" class=\"wp-image-3739\" style=\"width:244px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;2x<sup>2<\/sup>+9x+9=(x+3)(2x+3).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview.png\" alt=\"\" class=\"wp-image-3740\" style=\"width:276px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b4c3ee\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-b22ef48acde4c0a793483be00af02a19\" style=\"color:#b00012\">Which&nbsp;area model represents the factorization<\/p>\n\n\n\n<p>&nbsp;6x<sup>2<\/sup>+13x+6=(2x+3)(3x+2)?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4.png\" alt=\"\" class=\"wp-image-3752\" style=\"width:254px;height:254px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-3.png\" alt=\"\" class=\"wp-image-3753\" style=\"width:254px;height:254px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-3.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-3-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-1.png\" alt=\"\" class=\"wp-image-3754\" style=\"width:288px;height:288px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-1.png\" alt=\"\" class=\"wp-image-3755\" style=\"width:239px;height:239px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;area model represents the factorization&nbsp;6x<sup>2<\/sup>+13x+6=(2x+3)(3x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview.png\" alt=\"\" class=\"wp-image-3756\" style=\"width:283px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;left side of the equation represents the total area written as the sum of all the tiles. There are&nbsp;6<span style=\"text-decoration: underline;\">&nbsp;<em>x<\/em>2&nbsp;<\/span>tiles,&nbsp;13&nbsp;<em><span style=\"text-decoration: underline;\">x<\/span><\/em>&nbsp;tiles, and&nbsp;6<span style=\"text-decoration: underline;\">&nbsp;1<\/span>&nbsp;tiles, so the sum is&nbsp;6x<sup>2<\/sup>+13x+6.<\/p>\n\n\n\n<p>The&nbsp;right side of the equation represents the total area written as base times height. The base is made up of&nbsp;2&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;3&nbsp;1&nbsp;tiles, so it is&nbsp;(2x+3).&nbsp;The height is made up of&nbsp;3&nbsp;<span style=\"text-decoration: underline;\"><em>x<\/em>&nbsp;<\/span>tiles and&nbsp;2&nbsp;<span style=\"text-decoration: underline;\">1<\/span>&nbsp;tiles, so it is&nbsp;(3x+2).&nbsp;The base times the height is&nbsp;(2x+3)(3x+2).<\/p>\n\n\n\n<p>The&nbsp;other area models represent factorizations of different&nbsp;polynomials.<\/p>\n\n\n\n<p>This&nbsp;area model shows&nbsp;4x<sup>2<\/sup>+10x+6=(2x+3)(2x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3757\" style=\"width:289px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;6x<sup>2<\/sup>+15x+9=(2x+3)(3x+3).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3758\" style=\"width:324px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;4x<sup>2<\/sup>+12x+9=(2x+3)(2x+3).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3759\" style=\"width:222px;height:222px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#94e486\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-b22ef48acde4c0a793483be00af02a19\" style=\"color:#b00012\">Which&nbsp;area model represents the factorization<\/p>\n\n\n\n<p>&nbsp;3x<sup>2<\/sup>+6x+3=(3x+3)(x+1)?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px.png\" alt=\"\" class=\"wp-image-3764\" style=\"width:345px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-1.png\" alt=\"\" class=\"wp-image-3765\" style=\"width:350px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-1-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-2.png\" alt=\"\" class=\"wp-image-3766\" style=\"width:433px;height:173px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-2-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-3.png\" alt=\"\" class=\"wp-image-3767\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-3.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-3-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;area model represents the factorization&nbsp;3x<sup>2<\/sup>+6x+3=(3x+3)(x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___4_-removebg-preview.png\" alt=\"\" class=\"wp-image-3768\" style=\"aspect-ratio:2.504424778761062;width:388px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___4_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___4_-removebg-preview-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;left side of the equation represents the total area written as the sum of all the tiles. There are&nbsp;3&nbsp;<i><u>x 2<\/u><\/i>&nbsp;tiles,&nbsp;6&nbsp;<span style=\"text-decoration: underline;\"><em>x<\/em>&nbsp;<\/span>tiles, and&nbsp;3&nbsp;<span style=\"text-decoration: underline;\">1<\/span>&nbsp;tiles, so the sum is&nbsp;3x<sup>2<\/sup>+6x+3.<\/p>\n\n\n\n<p>The&nbsp;right side of the equation represents the total area written as base times height. The base comprises&nbsp;3&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;3&nbsp;1&nbsp;tiles, so it is&nbsp;(3x+3).&nbsp;The height is 1&nbsp;<em><span style=\"text-decoration: underline;\">x<\/span><\/em>&nbsp;tile and&nbsp;1&nbsp;<span style=\"text-decoration: underline;\">1<\/span>&nbsp;tile, so it is&nbsp;(x+1).&nbsp;The base times the height is&nbsp;(3x+3)(x+1).<\/p>\n\n\n\n<p>The&nbsp;other area models represent factorizations of different&nbsp;polynomials.<\/p>\n\n\n\n<p>This&nbsp;area model shows&nbsp;3x<sup>2<\/sup>+5x+2=(3x+2)(x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview.png\" alt=\"\" class=\"wp-image-3769\" style=\"width:325px;height:130px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;6x<sup>2<\/sup>+9x+3=(3x+3)(2x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px_-removebg-preview.png\" alt=\"\" class=\"wp-image-3770\" style=\"width:460px;height:184px\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px_-removebg-preview-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;6x<sup>2<\/sup>+7x+2=(3x+2)(2x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-3771\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview-1-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85395\/868\/252\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45.png\" alt=\"\" class=\"wp-image-6920\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-45-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-63.png\" alt=\"\" class=\"wp-image-6921\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-63.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-63-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-63-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Factorise quadratics using algebra tiles key notes: Learn with an example Which&nbsp;area model represents the factorization&nbsp; 3&#215;2+12x+9=(x+3)(3x+3)? This&nbsp;area model represents the factorization&nbsp;3&#215;2+12x+9=(x+3)(3x+3). The&nbsp;left side of the equation represents the total area written as the sum of all the tiles. There are&nbsp;3&nbsp;x2&nbsp;tiles,&nbsp;12&nbsp;x&nbsp;tiles, and&nbsp;9&nbsp;1&nbsp;tiles, so the sum is&nbsp;3&#215;2+12x+9. The&nbsp;right side of the equation represents the total area<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/i-6-factorise-quadratics-using-algebra-tiles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;I.6 Factorise quadratics using algebra tiles&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-178","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=178"}],"version-history":[{"count":15,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178\/revisions"}],"predecessor-version":[{"id":17450,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/178\/revisions\/17450"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}