{"id":1195,"date":"2013-06-06T08:43:07","date_gmt":"2013-06-06T08:43:07","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=1195"},"modified":"2026-03-25T12:35:43","modified_gmt":"2026-03-25T17:35:43","slug":"multiplying-terms-using-the-foil-method","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/multiplying-terms-using-the-foil-method\/","title":{"rendered":"Multiplying Terms Using the FOIL Method"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_jHVYuIEEDq8\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_jHVYuIEEDq8\" data-source-videoID=\"jHVYuIEEDq8\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Multiplying Terms Using the FOIL Method Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Multiplying Terms Using the FOIL Method\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_jHVYuIEEDq8:hover {cursor:pointer;} img#videoThumbnailImage_jHVYuIEEDq8 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1856-thumb-final-2-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_jHVYuIEEDq8\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_jHVYuIEEDq8\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Multiplying Terms Using the FOIL Method\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_jHVYuIEEDq8\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_jHVYuIEEDq8\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_jHVYuIEEDq8\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction rjR_Function() {\n  var x = document.getElementById(\"rjR\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"rjR_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"rjR\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Reviewing_Polynomials\" class=\"smooth-scroll\">Reviewing Polynomials<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#The_FOIL_Method\" class=\"smooth-scroll\">The FOIL Method<\/a>\n<ul><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<li class=\"toc-h3\"><a href=\"#Example_4\" class=\"smooth-scroll\">Example #4<\/a><\/li>\n<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#FOIL_Method_Practice_Questions\" class=\"smooth-scroll\">FOIL Method Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video about multiplying terms using the FOIL method.<\/p>\n<p>Today, we\u2019ll learn a strategy for multiplying two-digit numbers. We\u2019ll also learn how to apply this strategy to multiplying polynomials with two terms. <\/p>\n<h2><span id=\"Reviewing_Polynomials\" class=\"m-toc-anchor\"><\/span>Reviewing Polynomials<\/h2>\n<p>\nBefore we get started, let\u2019s review a few things. First, a polynomial is an expression that can have many terms with variables, coefficients, and positive exponents. These terms can be added, subtracted, multiplied, and divided. <\/p>\n<p>Today we\u2019re going to talk about polynomials with two terms. Polynomials with two terms are called <strong>binomials<\/strong>. <\/p>\n<p>Examples of binomials are \\(2x+7, 30\\text{ }+8,\\text{ and}\\text{ }5x^{2}-3\\). All binomials have two terms that are separated by an operation sign. <\/p>\n<h2><span id=\"The_FOIL_Method\" class=\"m-toc-anchor\"><\/span>The FOIL Method<\/h2>\n<p>\nThe FOIL method is a technique that\u2019s used to remember the steps for multiplying two binomials. The letters in the word FOIL stand for First, Outer, Inner, and Last. The product of two binomials is the sum of multiplying the first terms, outer terms, inner terms, and last terms: <\/p>\n<div class=\"examplesentence\">\\((a+b)(c+d)\\)\\(=ac+ad+bc+bd\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nLet\u2019s look at an example of multiplying two-digit numbers using the FOIL method. <\/p>\n<p>Consider the multiplication problem \\(35\\times 56\\). To solve using the FOIL method, start by writing each term as a binomial. In other words, split each number into two numbers according to their place value.<\/p>\n<p>So \\(35\\) is \\((30+5)\\) and \\(56\\) is \\((50+6)\\). <\/p>\n<p>Now that each number is written as a binomial, we can apply the FOIL method. <\/p>\n<p>So the F in FOIL stands for First. We\u2019re going to multiply our first terms by one another.<\/p>\n<div class=\"examplesentence\">\\(30\\times 50=1,500\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe O in FOIL stands for Outer, so we\u2019re going to multiply our outer numbers.<\/p>\n<div class=\"examplesentence\">\\(30\\times 6=180\\)<\/div>\n<p>\n&nbsp;<br \/>\nThe I in FOIL stands for Inner, so we\u2019re going to multiply the inner terms.<\/p>\n<div class=\"examplesentence\">\\(5\\times 50=250\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd finally, we have the L in FOIL, which stands for Last. So the last two terms of our binomials are 5 and 6.<\/p>\n<div class=\"examplesentence\">\\(5\\times 6=30\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, all we have to do is add this together and we\u2019ll get a total of: \\(1,500+180+250+30=1,960\\).<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s look at another multiplication problem where we can apply the FOIL method. <\/p>\n<div class=\"transcriptcallout\" style=\"text-align: left;\">Makayla has 24 filled photo albums. If each album holds 48 photos, how many photos does she have in all?<\/div>\n<p>\n&nbsp;<br \/>\nTo solve this problem, we need to multiply \\(24\\times 48\\). To solve using the FOIL method, start by writing each term as a binomial, so \\(24\\) is \\((20+4)\\) times 48 is \\((40+8)\\).<\/p>\n<div class=\"examplesentence\">\\((20+4)(40+8)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow that each number is written as a binomial, we can apply the FOIL method. <\/p>\n<p>The F in FOIL stands for First, so we\u2019ll multiply our first terms by one another.<\/p>\n<div class=\"examplesentence\">\\(20\\times 40=800\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen we\u2019ll do our outer terms because that\u2019s what the O stands for.<\/p>\n<div class=\"examplesentence\">\\(20\\times 8=160\\)<\/div>\n<p>\n&nbsp;<br \/>\nNext comes I, which stands for Inner.<\/p>\n<div class=\"examplesentence\">\\(4\\times 40=160\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd finally, we\u2019re going to do the L, which is the last two terms.<\/p>\n<div class=\"examplesentence\">\\(4\\times 8=32\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, all we have to do is add these four numbers together and we get: \\(800+160+160+32=1,152\\). So Makayla has 1,152 photos altogether. <\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nThe FOIL method is a good strategy for multiplying two-digit numbers, especially if you don\u2019t have a calculator on hand. The FOIL method can also be applied to binomials with variables and exponents. Let\u2019s look at another problem together: <\/p>\n<div class=\"examplesentence\">\\((6x+3)(4x+7)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNotice that this problem has the variable \\(x\\) in the terms \\(6x\\) and \\(4x\\). Even so, we can apply the FOIL method to multiply. <\/p>\n<p>So we\u2019re going to start by multiplying our first terms together.<\/p>\n<div class=\"examplesentence\">\\(6x\\times 4x=24x^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen we\u2019re going to multiply our outer terms.<\/p>\n<div class=\"examplesentence\">\\(6x\\times 7=42x\\)<\/div>\n<p>\n&nbsp;<br \/>\nNext, we\u2019ll do our inner terms, which is \\(3\\) and \\(4x\\).<\/p>\n<div class=\"examplesentence\">\\(3\\times 4x=12x\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd finally, we\u2019ll do our last terms.<\/p>\n<div class=\"examplesentence\">\\(3\\times 7=21\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow all we have to do is add our like terms right here.<\/p>\n<div class=\"examplesentence\">\\(24x^{2}+42x+12x+21\\)<\/div>\n<p>\n&nbsp;<\/p>\n<div class=\"examplesentence\">\\(24x^{2}+54x+21\\)<\/div>\n<p>\n&nbsp;<br \/>\nSo that\u2019s our answer: \\(24x^{2}+54x+21\\). <\/p>\n<h3><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h3>\n<p>\nI have one more problem for you to analyze on your own. This one is a little bit more challenging, but I know you can do it. <\/p>\n<div class=\"transcriptcallout\" style=\"text-align: left;\">The length of a rectangle is \\((5x+1)\\). Its width is \\((2x+8)\\). Write a polynomial for the area of the rectangle in standard form, \\(ax^{2}+bx+c\\).<\/div>\n<p>\n&nbsp;<br \/>\nPause the video, analyze the word problem, and see if you can solve it by yourself. When you\u2019re ready, resume the video, and we\u2019ll go over the answer together. <\/p>\n<p>Now that you\u2019ve tried this problem, let\u2019s go over it together. <\/p>\n<p>To find the area of a rectangle, multiply its length by its width. <\/p>\n<div class=\"examplesentence\">\\(A=lw\\)<\/div>\n<p>\n&nbsp;<br \/>\nSince the length is \\((5x+1)\\), we can write that. And the width is \\((2x+8)\\).<\/p>\n<div class=\"examplesentence\">\\(A=(5x+1)(2x+8)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we can multiply using the FOIL method.<\/p>\n<p>So the first two terms are \\(5x\\) and \\(2x\\).<\/p>\n<div class=\"examplesentence\">\\(5x\\times 2x=10x^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nPlus our outer terms.<\/p>\n<div class=\"examplesentence\">\\(5x\\times 8=40x\\)<\/div>\n<p>\n&nbsp;<br \/>\nPlus our inner terms.<\/p>\n<div class=\"examplesentence\">\\(1\\times 2x=2x\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd finally, our last terms.<\/p>\n<div class=\"examplesentence\">\\(1\\times 8=8\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe add all these together.<\/p>\n<div class=\"examplesentence\">\\(10&#215;2+40x+2x+8\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow all we have to do is combine our like terms. <\/p>\n<div class=\"examplesentence\">\\(10&#215;2+42x+8\\)<\/div>\n<p>\n&nbsp;<br \/>\nTherefore, the area of the rectangle is \\(10x^{2}+42x+8\\). <\/p>\n<p>Great job!<\/p>\n<p>I hope this video about multiplying terms using the FOIL method was helpful. Thanks for watching, and happy studying! <\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"FOIL_Method_Practice_Questions\" class=\"m-toc-anchor\"><\/span>FOIL Method Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSolve the following equation using the FOIL method:<\/p>\n<div class=\"yellow-math-quote\">\\(48 \\times 72=\\) ?<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">936<\/div><div class=\"PQ\"  id=\"PQ-1-2\">1,264<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">3,456<\/div><div class=\"PQ\"  id=\"PQ-1-4\">3,650<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The product of two binomials is the sum of multiplying the first terms, outer terms, inner terms, and last terms.<\/p>\n<p>Before applying the FOIL method, start by writing each term as a binomial.<\/p>\n<p style=\"text-align: center\">\\((40+8)(70+2)\\)<\/p>\n<p>Next, multiply the first terms.<\/p>\n<p style=\"text-align: center\">\\(40\\times70=2{,}800\\)<\/p>\n<p>Then, multiply the outer terms.<\/p>\n<p style=\"text-align: center\">\\(40\\times2=80\\)<\/p>\n<p>From here, multiply the inner terms.<\/p>\n<p style=\"text-align: center\">\\(8\\times70=560\\)<\/td>\n<p>After that, multiply the last terms.<\/p>\n<p style=\"text-align: center\">\\(8\\times2=16\\)<\/p>\n<p>Finally, add the products together to get a total of 3,456.<\/p>\n<p style=\"text-align: center\">\\(2{,}800+80+560+16=3{,}456\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nMultiply the binomials below using the FOIL method. Write your answer in standard form (\\(ax^2+bx+c\\)).<\/p>\n<div class=\"yellow-math-quote\">\\((7x+8)(2x+1)\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">\\(14x^2+9x+9\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(32x+8\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(9x^2+23x+8\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">\\(14x^2+23x+8\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The product of two binomials is the sum of multiplying the first terms, outer terms, inner terms, and last terms.<\/p>\n<p>Start applying the FOIL method by multiplying the first two terms.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\((7x+8)(2x+1)\\)<br \/>\n\\(7x\\cdot2x=14x^3\\)<\/p>\n<p>Next, multiply the outer terms.<\/p>\n<p style=\"text-align: center\">\\(7x\\cdot1=7x\\)<\/p>\n<p>Then, multiply the inner terms.<\/p>\n<p style=\"text-align: center\">\\(8\\cdot2x=16x\\)<\/p>\n<p>From here, multiply the last terms.<\/p>\n<p style=\"text-align: center\">\\(8\\cdot1=8\\)<\/p>\n<p>Create one expression by adding the partial products together.<\/p>\n<p style=\"text-align: center\">\\(14x^2+7x+16x+8\\)<\/p>\n<p>Finally, write the expression in standard form by combining like terms.<\/p>\n<p style=\"text-align: center\">\\(14x^2+23x+8\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nMultiply the binomials below using the FOIL method. Write your answer in standard form (\\(ax^2+bx+c\\)).<\/p>\n<div class=\"yellow-math-quote\">\\((x-4)(2x+9)\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(3x^2-x-36\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">\\(2x^2+x-36\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(2x^2-x+36\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\(3x^2+x+36\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The product of two binomials is the sum of multiplying the first terms, outer terms, inner terms, and last terms.<\/p>\n<p>Start applying the FOIL method by multiplying the first two terms.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\((x-4)(2x+9)\\)<br \/>\n\\(x\\cdot2x=2x^2\\)<\/p>\n<p>Next, multiply the outer terms.<\/p>\n<p style=\"text-align: center\">\\(x\\cdot9=9x\\)<\/p>\n<p>Then, multiply the inner terms.<\/p>\n<p style=\"text-align: center\">\\(-4\\cdot2x=-8x\\)<\/p>\n<p>From here, multiply the last terms.<\/p>\n<p style=\"text-align: center\">\\(-4\\cdot9=-36\\)<\/p>\n<p>Create one expression by adding the partial products together.<\/p>\n<p style=\"text-align: center\">\\(2x^2+9x-8x-36\\)<\/p>\n<p>Finally, write the expression in standard form by combining like terms.<\/p>\n<p style=\"text-align: center\">\\(2x^2+x-36\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSal is planting a vegetable garden in his backyard. The length of the garden is \\((3x+4)\\). Its width is \\((2x-5)\\). Use the FOIL method to write a polynomial for the area of the garden. Write your answer in standard form (\\(ax^2+bx+c\\)).<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\(5x^2-7x+20\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(6x^2+7x-20\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(5x^2+7x+20\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">\\(6x^2-7x-20\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the area of the garden, multiply the length by the width. Since both measurements are given as binomials, we can apply the FOIL method to solve. The product of two binomials is the sum of multiplying the first terms, outer terms, inner terms, and last terms.<\/p>\n<p>Start applying the FOIL method by multiplying the first two terms.<\/p>\n<p style=\"text-align: center; line-height: 35px\">\\((3x+4)(2x-5)\\)<br \/>\n\\(3x\\cdot2x=6x^2\\)<\/p>\n<p>Next, multiply the outer terms.<\/p>\n<p style=\"text-align: center\">\\(3x\\cdot(-5)=-15x\\)<\/p>\n<p>Then, multiply the inner terms.<\/p>\n<p style=\"text-align: center\">\\(4\\cdot2x=8x\\)<\/p>\n<p>From here, multiply the last terms.<\/p>\n<p style=\"text-align: center\">\\(4\\cdot(-5)=-20\\)<\/p>\n<p>Create one expression by adding the partial products together.<\/p>\n<p style=\"text-align: center\">\\(6x^2-15x+8x-20\\)<\/p>\n<p>Finally, write the expression in standard form by combining like terms.<\/p>\n<p style=\"text-align: center\">\\(6x^2-7x-20\\)<\/p>\n<p>Therefore, the area of Sal\u2019s vegetable garden is \\(6x^2-7x-20\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>Shannon is shopping for doormats. The length of her current rectangular doormat is 3 times longer than its width, \\(w\\). She wants to get a new doormat that is 1.5 feet longer and 1.5 feet wider than her current doormat. Write an expression with two binomials that represents this scenario. Then, multiply the binomials using the FOIL method to write a polynomial for the area of the new doormat. Write your answer in standard form (\\(ax^2+bx+c\\)). <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(3w^2+60w+225\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">\\(3w^2+6w+2.25\\)<\/div><div class=\"PQ\"  id=\"PQ-5-3\">\\(4w^2+3w+3\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(4w^2+3w+2.25\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>To find the area of the new doormat, multiply the length by the width. Since the new doormat\u2019s width is 1.5 feet wider than the old doormat, the width is \\((w+1.5)\\). Since the new doormat\u2019s length is 3 times the original width and 1.5 feet longer than the old doormat, the length is \\((3w+1.5)\\).<\/p>\n<p style=\"text-align: center;\">\\((w+1.5)(3w+1.5)\\)<\/p>\n<p>Since both measurements are given as binomials, we can apply the FOIL method to solve. The product of two binomials is the sum of multiplying the first terms, outer terms, inner terms, and last terms.<\/p>\n<p>Start applying the FOIL method by multiplying the first two terms.<\/p>\n<p style=\"text-align: center;\">\\(w\\cdot3w=3w^2\\)<\/p>\n<p>Next, multiply the outer terms. <\/p>\n<p style=\"text-align: center;\">\\(w\\cdot1.5=1.5w\\)<\/p>\n<p>Then, multiply the inner terms.<\/p>\n<p style=\"text-align: center;\">\\(1.5\\cdot3w=4.5w\\)<\/p>\n<p>From here, multiply the last terms.<\/p>\n<p style=\"text-align: center;\">\\(1.5\\cdot1.5=2.25\\)<\/p>\n<p>Create one expression by adding the partial products together.<\/p>\n<p style=\"text-align: center;\">\\(3w^2+1.5w+4.5w+2.25\\)<\/p>\n<p>Finally, write the expression in standard form by combining like terms.<\/p>\n<p style=\"text-align: center;\">\\(3w^2+6w+2.25\\)<\/p>\n<p>Therefore, the area of Shannon\u2019s new doormat is \\(3w^2+6w+2.25\\text{ ft}\\).<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-i\/\">Return to Algebra I Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra I Videos<\/p>\n","protected":false},"author":1,"featured_media":98350,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-1195","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-algebra-basics-videos","7":"page_category-math-advertising-group","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO Pro 4.9.8 - aioseo.com -->\n\t<meta name=\"description\" content=\"Multiplying using FOIL simplifies complex problems with or without variables. 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