{"id":122983,"date":"2022-05-30T10:06:18","date_gmt":"2022-05-30T15:06:18","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=122983"},"modified":"2026-03-28T11:53:05","modified_gmt":"2026-03-28T16:53:05","slug":"factoring-the-difference-of-two-squares","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/factoring-the-difference-of-two-squares\/","title":{"rendered":"Factoring the Difference of Two Squares"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_d4_zjhrE5Oc\" 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_d4_zjhrE5Oc\" data-source-videoID=\"d4_zjhrE5Oc\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Factoring the Difference of Two Squares Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Factoring the Difference of Two Squares\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_d4_zjhrE5Oc:hover {cursor:pointer;} img#videoThumbnailImage_d4_zjhrE5Oc {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/2345-thumbnail-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_d4_zjhrE5Oc\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_d4_zjhrE5Oc\" 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\",\"Factoring the Difference of Two Squares\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_d4_zjhrE5Oc\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_d4_zjhrE5Oc\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_d4_zjhrE5Oc\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction 8hn_Function() {\n  var x = document.getElementById(\"8hn\");\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=\"8hn_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=\"8hn\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Example_1\" class=\"smooth-scroll\">Example #1<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_2\" class=\"smooth-scroll\">Example #2<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_3\" class=\"smooth-scroll\">Example #3<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Example_4\" class=\"smooth-scroll\">Example #4<\/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>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello, and welcome to this video on factoring the difference of two squares.<\/p>\n<p>When factoring polynomials, there are a few special patterns you\u2019ll want to be on the lookout for. The one we\u2019ll be talking about in this video is the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/difference-of-squares\/\">difference of two squares<\/a>. <\/p>\n<p>When you see a binomial in the form \\(a^{2}-b^{2}\\), then you know you are looking at a difference of two squares, and it will factor to \\((a+b)(a-b)\\). The reason there\u2019s no middle term is because FOILing these binomials will result in the outer and inner terms canceling each other out.<\/p>\n<div class=\"examplesentence\">\\(a^{2}-ab+ab-b^{2}\\)<br \/>\n\\(a^{2}-b^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nLet\u2019s look at a few examples.<\/p>\n<h2><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h2>\n<div class=\"examplesentence\">\\(x^{2}-4\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe know this is an example of a difference of two squares because it is a binomial with a subtraction sign between the two terms, and both terms are perfect squares. To factor this binomial, take the positive square root of both terms (ignoring the minus sign).<\/p>\n<div class=\"examplesentence\">\\(\\sqrt{x^{2}}=x\\) <br \/>\n\\(\\sqrt{4}=2\\)<\/div>\n<p>\n&nbsp;<br \/>\nRemember, a difference of squares binomial factors to \\((a+b)(a-b)\\). In this case, \\(a=x\\) and \\(b=2\\), so the factored form is:<\/p>\n<div class=\"examplesentence\">\\((x+2)(x-2)\\)<\/div>\n<p>\n&nbsp;<br \/>\nIf you wanted to check your answer, you can always <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/multiplying-terms-using-the-foil-method\/\">FOIL<\/a> it and see if you get the original expression.<\/p>\n<h2><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h2>\n<p>\nLet\u2019s try another one.<\/p>\n<div class=\"examplesentence\">\\(x^{2}-36\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, check that this matches the pattern \\(a^{2}-b^{2}\\). It does, so take the square root of both terms.<\/p>\n<div class=\"examplesentence\">\\(a=\\sqrt{x^{2}}=x\\)<br \/>\n\\(b=\\sqrt{36}=6\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, write out the factored form of the binomial.<\/p>\n<div class=\"examplesentence\">\\((x+6)(x-6)\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h2>\n<p>\nLet\u2019s try one that\u2019s slightly harder.<\/p>\n<div class=\"examplesentence\">\\(4y^{2}-16\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, check that this matches the pattern \\(a^{2}-b^{2}\\). It looks different from our other examples, but this does follow this pattern because \\(4y^{2}\\) is a perfect square.<\/p>\n<p>Take the positive square root of both terms.<\/p>\n<div class=\"examplesentence\">\\(a=\\sqrt{4y^{2}}=2y\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we know that \\(2y\\) is the positive square root of \\(4y^{2}\\) because we&#8217;re going to take the square root of our coefficient 4, \\(\\sqrt{4}=2\\), and then multiply it by \\(y^{2}\\), which is \\(y\\). So that&#8217;s how we simplify this.<\/p>\n<div class=\"examplesentence\">\\(b=\\sqrt{16}=4\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, create the factored form of the binomial.<\/p>\n<div class=\"examplesentence\">\\((2y+4)(2y-4)\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h2><span id=\"Example_4\" class=\"m-toc-anchor\"><\/span>Example #4<\/h2>\n<p>\nLet\u2019s work through one more example before we go.<\/p>\n<div class=\"examplesentence\">\\(16a^{4}-49\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, make sure it follows the pattern \\(a^{2}-b^{2}\\). Since it does, take the positive square root of both terms. So remember, to take the square root of an expression like this \\((16a^{4})\\), take the square root of the coefficient first. \\(\\sqrt{16}=4\\), and then \\(\\sqrt{a^{4}}=a^{2}\\), so we&#8217;ll have \\(4a^{2}\\).<\/p>\n<div class=\"examplesentence\">\\(a=\\sqrt{16a^{4}}=4a^{2}\\)<br \/>\n\\(b=\\sqrt{49}=7\\)<\/div>\n<p>\n&nbsp;<br \/>\nThen, write the factored form of the binomial.<\/p>\n<div class=\"examplesentence\">\\((4a^{2}+7)(4a^{2}-7)\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd there you have it! Now you should be more comfortable recognizing difference of squares problems and how to factor them.<\/p>\n<p>I hope this video was helpful. Thanks for watching, and happy studying!<\/p>\n<\/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":22,"featured_media":122986,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-122983","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/122983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=122983"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/122983\/revisions"}],"predecessor-version":[{"id":281267,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/122983\/revisions\/281267"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/122986"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=122983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}