{"id":158,"date":"2022-04-13T10:11:26","date_gmt":"2022-04-13T10:11:26","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=158"},"modified":"2025-01-18T08:36:47","modified_gmt":"2025-01-18T08:36:47","slug":"h-9-multiply-two-polynomials-using-algebra-tiles","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/h-9-multiply-two-polynomials-using-algebra-tiles\/","title":{"rendered":"H.9 Multiply two polynomials 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> Multiply two polynomials using algebra tiles<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-04d9d6410ea0aa79bd5fd62d138d8458\" 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>Understand Basic Algebra Tiles:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Algebra tiles represent variables and constants visually. Typically, squares represent constants, and rectangles represent variables.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Model Each Term:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Break down each polynomial into its individual terms.<\/li>\n\n\n\n<li>Use tiles to model each term, considering the appropriate shape and size for variables and constants.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Arrange Tiles for Each Polynomial:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Lay out the tiles for one polynomial horizontally and the tiles for the other polynomial vertically.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Multiply Each Pair of Tiles:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Multiply each pair of tiles, considering both the numerical and variable components.<\/li>\n\n\n\n<li>For example, the product of a constant tile (square) and a variable tile (rectangle) is the product of their numerical coefficients and the product of their variables.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Combine Like Terms:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Combine the tiles with the same variable and exponent to simplify the expression.<\/li>\n\n\n\n<li>Arrange the tiles neatly to represent the final product.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Count Tiles to Determine Coefficients:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Count the number of tiles in each region to determine the coefficients of the terms in the final product.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Illustrate the Distributive Property:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Emphasize the connection between the visual model and the distributive property.<\/li>\n\n\n\n<li>Show how each term in one polynomial is multiplied by each term in the other polynomial.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Practice with Examples:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Work through several examples with different polynomials to reinforce the understanding of the process.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Check the Result:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Validate the final result by multiplying the polynomials using the traditional algebraic method to ensure consistency.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Use Algebra Tiles as a Learning Tool:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Encourage students to use algebra tiles as a tool to visualize and understand polynomial multiplication, especially when introducing the topic.<\/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\" style=\"background-color:#eca5a5\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-large-font-size\">Which&nbsp;multiplication expression does this area model&nbsp;represent?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"355\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-28.png\" alt=\"\" class=\"wp-image-11220\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-28.png 193w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-28-163x300.png 163w\" sizes=\"auto, (max-width: 193px) 100vw, 193px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">(x+2) (3x+3)          (2x+2) (3x+3)<\/p>\n\n\n\n<p class=\"has-large-font-size\">(x+1) (3x+3)           (2x+3) (3x+3)<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-large-font-size\">Look&nbsp;at the base. The base is made up of&nbsp;1&nbsp;<strong><em>x<\/em>&nbsp;<\/strong>tile and&nbsp;2&nbsp;<strong>1&nbsp;<\/strong>tiles. So, the base represents (x+2)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"387\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-5.png\" alt=\"\" class=\"wp-image-11261\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-5.png 162w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-5-126x300.png 126w\" sizes=\"auto, (max-width: 162px) 100vw, 162px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">Next,&nbsp;look at the height. The height is made up of&nbsp;3&nbsp;<em>x<\/em><strong>&nbsp;<\/strong>tiles and&nbsp;3&nbsp;<strong>1&nbsp;<\/strong>tiles. So, the height represents (3x+3)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"254\" height=\"371\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-6.png\" alt=\"\" class=\"wp-image-11262\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-6.png 254w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-6-205x300.png 205w\" sizes=\"auto, (max-width: 254px) 100vw, 254px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">Finally,&nbsp;multiply the base and the height. This area model represents (x+2) (3x+3)<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#ea95ee\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-48cb86769c66b878714027326c43f652\" style=\"color:#b00012\">Which&nbsp;area model represents the expression (3x+1) (x+2)?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"415\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-31.png\" alt=\"\" class=\"wp-image-11246\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-31.png 369w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-31-267x300.png 267w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"417\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-32.png\" alt=\"\" class=\"wp-image-11247\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-32.png 383w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-32-276x300.png 276w\" sizes=\"auto, (max-width: 383px) 100vw, 383px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p class=\"has-large-font-size\">This&nbsp;is the area model that represents the expression (3x+1) (x+2)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"185\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-7.png\" alt=\"\" class=\"wp-image-11263\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-7.png 355w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-7-300x156.png 300w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">Look&nbsp;at the base. The base is made up of&nbsp;3&nbsp;<strong><em>x<\/em>&nbsp;<\/strong>tiles and&nbsp;1&nbsp;<strong>1&nbsp;<\/strong>tile. So, the base represents (3x+1)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"210\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-8.png\" alt=\"\" class=\"wp-image-11264\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-8.png 346w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-8-300x182.png 300w\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" \/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">Next,&nbsp;look at the height. The height is made up of&nbsp;1&nbsp;<strong><em>x<\/em>&nbsp;<\/strong>tile and&nbsp;2&nbsp; <strong>1&nbsp;<\/strong>tiles. So, the height represents (x+2)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"414\" height=\"183\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-9.png\" alt=\"\" class=\"wp-image-11265\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-9.png 414w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-9-300x133.png 300w\" sizes=\"auto, (max-width: 414px) 100vw, 414px\" \/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">Finally,&nbsp;multiply the base and the height. This area model represents&nbsp;(3x+1)(x+2)<\/p>\n\n\n\n<p class=\"has-large-font-size\">The&nbsp;other area models represent different&nbsp;expressions.<\/p>\n\n\n\n<p class=\"has-large-font-size\">This&nbsp;area model represents(2x+1) (x+3)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"267\" height=\"228\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-10.png\" alt=\"\" class=\"wp-image-11266\"\/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">This&nbsp;area model represents (3x+1) (x+1)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"336\" height=\"150\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-11.png\" alt=\"\" class=\"wp-image-11267\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-11.png 336w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-11-300x134.png 300w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/figure>\n\n\n\n<p class=\"has-large-font-size\">This&nbsp;area model represents(2x+1)(x+2)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"253\" height=\"167\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/image-removebg-preview-12.png\" alt=\"\" class=\"wp-image-11268\"\/><\/figure>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!\ud83d\udd8a\ufe0f<\/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\/85171\/330\/643\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36.png\" alt=\"\" class=\"wp-image-6860\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-36-150x150.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\"><a href=\"https:\/\/wordwall.net\/play\/51763\/376\/658\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54.png\" alt=\"\" class=\"wp-image-6862\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-54-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply two polynomials using algebra tiles key notes: Learn with an example Which&nbsp;multiplication expression does this area model&nbsp;represent? (x+2) (3x+3) (2x+2) (3x+3) (x+1) (3x+3) (2x+3) (3x+3) Look&nbsp;at the base. The base is made up of&nbsp;1&nbsp;x&nbsp;tile and&nbsp;2&nbsp;1&nbsp;tiles. So, the base represents (x+2) Next,&nbsp;look at the height. The height is made up of&nbsp;3&nbsp;x&nbsp;tiles and&nbsp;3&nbsp;1&nbsp;tiles. So, the height<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/h-9-multiply-two-polynomials-using-algebra-tiles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.9 Multiply two polynomials 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-158","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/158","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=158"}],"version-history":[{"count":13,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/158\/revisions"}],"predecessor-version":[{"id":17421,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/158\/revisions\/17421"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}