{"id":114722,"date":"2022-02-24T11:06:47","date_gmt":"2022-02-24T17:06:47","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/simplifying-algebraic-expressions-with-parentheses\/"},"modified":"2026-03-28T11:48:40","modified_gmt":"2026-03-28T16:48:40","slug":"simplifying-algebraic-expressions-with-parentheses","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/simplifying-algebraic-expressions-with-parentheses\/","title":{"rendered":"Simplifying Algebraic Expressions with Parentheses"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_X6S-Bl0dbjs\" 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_X6S-Bl0dbjs\" data-source-videoID=\"X6S-Bl0dbjs\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Simplifying Algebraic Expressions with Parentheses Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Simplifying Algebraic Expressions with Parentheses\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_X6S-Bl0dbjs:hover {cursor:pointer;} img#videoThumbnailImage_X6S-Bl0dbjs {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/2175-thumbnail-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_X6S-Bl0dbjs\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_X6S-Bl0dbjs\" 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\",\"Simplifying Algebraic Expressions with Parentheses\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_X6S-Bl0dbjs\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_X6S-Bl0dbjs\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_X6S-Bl0dbjs\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction j6D_Function() {\n  var x = document.getElementById(\"j6D\");\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=\"j6D_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=\"j6D\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Like_Terms\" class=\"smooth-scroll\">Like Terms<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Simplifying_Expressions\" class=\"smooth-scroll\">Simplifying Expressions<\/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<\/ul>\n<\/li>\n<li class=\"toc-h2\"><a href=\"#Simplifying_Algebraic_Expression_Practice_Questions\" class=\"smooth-scroll\">Simplifying Algebraic Expression 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! Today we\u2019re going to take a look at simplifying algebraic expressions with parentheses. <\/p>\n<h2><span id=\"Like_Terms\" class=\"m-toc-anchor\"><\/span>Like Terms<\/h2>\n<p>\nBefore we do that, let\u2019s review what like terms are. <strong>Like terms<\/strong> are any two terms that have the same variable raised to the same exponent.<\/p>\n<p>Some examples are:<\/p>\n<div class=\"examplesentence\">\\(x^{2}\\) and \\(7x^{2}\\)<br \/>\n\\(3xy\\) and \\(4xy\\)<br \/>\n\\(2x\\) and \\(5x\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow, an example of two terms that are not like terms would be:<\/p>\n<div class=\"examplesentence\">\\(6x\\) and  \\(6x^{2}\\)<\/div>\n<p>\n&nbsp;<br \/>\nEven though they have the same coefficient and the same variable, the variables are not raised to the same power, so these two terms are not like terms.<\/p>\n<p>The coefficient for like terms can be different; in fact, they usually are. For example, \\(2x\\) and \\(5x\\) are like terms, even though the coefficient 2 is different from the coefficient 5.<\/p>\n<h2><span id=\"Simplifying_Expressions\" class=\"m-toc-anchor\"><\/span>Simplifying Expressions<\/h2>\n<p>\nNow that we\u2019ve reviewed what like terms are, let\u2019s use this information to simplify some expressions. <\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nWe\u2019re going to start with this expression:<\/p>\n<div class=\"examplesentence\">\\((3x^{2}+2x-5)\\)\\(+(7x^{2}-3x+14)\\)<\/div>\n<p>\n&nbsp;<br \/>\nSince all our terms are being added or subtracted, we can use the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/associative-property\/\">associative and commutative properties<\/a> to regroup our terms so our like terms are next to one another. Remember, subtracting can be thought of as adding a negative, so these properties will still work. <\/p>\n<p>So, let&#8217;s combine our like terms. Our like terms are \\(3x^{2}\\) and \\(7x^{2}\\), \\(2x\\) and \\(-3x\\), and \\(-5\\) and \\(14\\). So we&#8217;re going to regroup and write them this way:<\/p>\n<div class=\"examplesentence\">\\((3^{2}+7x)+(2x-3x)\\)\\(+(-5+14)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we can simplify each set of parentheses.<\/p>\n<div class=\"examplesentence\">\\(10x^{2}+(-x)+9\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we can simplify this just a little bit further by changing this &#8220;adding a negative number&#8221; to just subtracting. So our final answer is going to be:<\/p>\n<div class=\"examplesentence\">\\(10x^{2}-x+9\\)<\/div>\n<p>\n&nbsp;<br \/>\nSince this isn&#8217;t an equation, we can\u2019t solve for anything. The most we can do is simplify, so this is our final answer.<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try another example.<\/p>\n<div class=\"examplesentence\">\\((x-17x)+(2xy-9xy)\\)\\(+(-3y+27y)\\)<\/div>\n<p>\n&nbsp;<br \/>\nFirst, we regroup our terms so our like terms are together. So let&#8217;s start by underlining our like terms. We have \\(x\\) and \\(-17x\\) as like terms, \\(2xy\\) and \\(-9xy\\) are like terms, and \\(-3y\\) and \\(27y\\) are also like terms. So now we can write them in parentheses.<\/p>\n<div class=\"examplesentence\">\\((x-17x)+(2xy-9xy)\\)\\(+(-3y+27y)\\)<\/div>\n<p>\n&nbsp;<\/p>\n<p>And now all we have to do is simplify each set of parentheses.<\/p>\n<div class=\"examplesentence\">\\(-16x-7xy+24y\\)<\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_3\" class=\"m-toc-anchor\"><\/span>Example #3<\/h3>\n<p>\nBefore we go, I want to try one more example that\u2019s slightly more difficult.<\/p>\n<div class=\"examplesentence\">\\((6x^{2}+4x-2)\\)\\(-(2x^{2}-18x+5)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNotice that this expression has a minus sign between the two sets of parentheses. Remember how I said earlier that subtracting is the same thing as adding a negative? This will help us in simplifying this expression. Let\u2019s rewrite it like this:<\/p>\n<div class=\"examplesentence\">\\((6x^{2}+4x-2)\\)\\(+(-1)(2x^{2}+18x-5)\\)<\/div>\n<p>\n&nbsp;<br \/>\nThis is where the adding a negative number comes in. But the negative number has to be 1 because that doesn&#8217;t change the value of the actual expression; 1 times anything is the original expression. So, this doesn&#8217;t change the value of anything, it just makes it look slightly different so we can understand where our next steps come from.<\/p>\n<p>Now that we have a negative 1 here, we need to distribute this negative 1 into each term in the second set of parentheses. So, we&#8217;re going to leave this first set of parentheses exactly the same, and distribute the -1 to the second set.<\/p>\n<div class=\"examplesentence\">\\((6x^{2}+4x-2)\\)\\(+(-2x^{2}+18x-5)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNotice that we have the exact same set of parentheses, just the sign has changed in front of each term. Now we&#8217;re going to follow the exact same steps as we have before. We&#8217;re going to underline our like terms, so we have \\(6x^{2}\\) and \\(-2x^{2}\\). \\(4x\\) and \\(18x\\) are also like terms, and so are -2 and -5. So now we&#8217;re going to regroup these like terms into their own sets of parentheses.<\/p>\n<div class=\"examplesentence\">\\((6x^{2}-2x^{2})+(4x-18x)\\)\\(+(-2-5)\\)<\/div>\n<p>\n&nbsp;<br \/>\nNow we&#8217;ll simplify each set of parentheses.<\/p>\n<div class=\"examplesentence\">\\(4x^{2}+22x-7\\)<\/div>\n<p>\n&nbsp;<br \/>\nAnd there you have it! I hope this video made this topic more understandable for you. Thanks for watching and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Simplifying_Algebraic_Expression_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Simplifying Algebraic Expression 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 \/>\nCompletely simplify the following expression:<\/p>\n<div class=\"yellow-math-quote\">\\((5x^2-7x+6)+(3x^2+4x+8)\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(9x^2-4x-2\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">\\({8x}^2-3x+14\\)<\/div><div class=\"PQ\"  id=\"PQ-1-3\">\\({2x}^2+3x+2\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\({8x}^2+3x+14\\)<\/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>To simplify an algebraic expression, we want to combine like terms. Like terms are terms whose variables with any exponents are the same.<\/p>\n<p>First, regroup the terms by using the associative and commutative properties of addition so our like terms are together.<\/p>\n<p style=\"text-align: center;\">\\((5x^2+3x^2)+(-7x+4x)+(6+8)\\)<\/p>\n<p>Now, simplify each group of like terms by combing them.<\/p>\n<p style=\"text-align: center;\">\\(8x^2+(-3x)+14\\)<\/p>\n<p>Lastly, \\(+(-3x)\\) simplifies to \\(-3x\\).<\/p>\n<p style=\"text-align: center;\">\\(8x^2-3x+14\\)<\/p>\n<p>There are no more like terms to combine, the expression is completely simplified.<\/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 \/>\nCompletely simplify the following expression:<\/p>\n<div class=\"yellow-math-quote-long\">\\((16x-9xy+13y)+(-12x+6xy-8y)\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-2-1\">\\(4x-3xy+5y\\)<\/div><div class=\"PQ\"  id=\"PQ-2-2\">\\(-4x+3xy+5y\\)<\/div><div class=\"PQ\"  id=\"PQ-2-3\">\\(28x-3xy-5y\\)<\/div><div class=\"PQ\"  id=\"PQ-2-4\">\\(22x-18xy-5y\\)<\/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>To simplify an algebraic expression, we want to combine like terms. Like terms are terms whose variables with any exponents are the same.<\/p>\n<p>First, regroup the terms by using the associative and commutative properties of addition so our like terms are together.<\/p>\n<p class=\"longmath\" style=\"text-align: center;\">\\((16x-12x)+(-9xy+6xy)+(13y-8y)\\)<\/p>\n<p>Now, simplify each group of like terms by combing them.<\/p>\n<p style=\"text-align: center;\">\\(4x+(-3xy)+5y\\)<\/p>\n<p>Lastly, simplify \\(+(-3xy)\\) to \\(-3xy\\).<\/p>\n<p style=\"text-align: center;\">\\(4x-3xy+5y\\)<\/p>\n<p>Since there are no more like terms to combine, the expression is completely simplified.<\/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 \/>\nCompletely simplify the following expression:<\/p>\n<div class=\"yellow-math-quote\">\\((6x^2+2x+7)-({2x}^2-5x+13)\\)<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\({8x}^2+7x-6\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\({8x}^2-3x+20\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">\\({4x}^2+7x-6\\)<\/div><div class=\"PQ\"  id=\"PQ-3-4\">\\({4x}^2+3x+20\\)<\/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>To simplify an algebraic expression, we want to combine like terms. Like terms are terms whose variables with any exponents are the same.<\/p>\n<p>Before combining like terms, we can change the subtraction sign between the two expressions to an addition sign by \u201cadding the negative of it.\u201d<\/p>\n<p style=\"text-align: center;\">\\((6x^2+2x+7)\\)\\(+(-1)({2x}^2-5x+13)\\)<\/p>\n<p>The \u22121 gets distributed to the second expression to give us:<\/p>\n<p style=\"text-align: center;\">\\((6x^2+2x+7)\\)\\(+(-{2x}^2+5x-13)\\)<\/p>\n<p>Now, regroup the terms by using the associative and commutative properties of addition so our like terms are together.<\/p>\n<p style=\"text-align: center;\">\\((6x^2-2x^2)\\)\\(+(2x+5x)+(7-13)\\)<\/p>\n<p>Simplify each group of like terms by combing them.<\/p>\n<p style=\"text-align: center;\">\\(4x^2+7x+(-6)\\)<\/p>\n<p>Lastly, simplify \\(+(-6)\\) to \\(-6\\).<\/p>\n<p style=\"text-align: center;\">\\(4x^2+7x-6\\)<\/p>\n<p>There are no more like terms to combine, the expression is completely simplified. <\/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 \/>\nSuppose the area, in square feet, of a square can be represented by the algebraic expression \\(16x^2+48x+36\\), and the area, in square feet, of a rectangle can be represented by the algebraic expression \\(5x^2-54x+40\\). Which of the following algebraic expressions represents the combined area of the square and rectangle?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">\\({53x}^2-38x+76\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(-38x^2+53x+76\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(21x^2+6x+76\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">\\(21x^2-6x+76\\)<\/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 combined area of the square and the rectangle, we need to add the two expressions that represent their respective areas.<\/p>\n<p style=\"text-align: center;\">\\((16x^2+48x+36)\\)\\(+(5x^2-54x+40)\\)<\/p>\n<p>To simplify the algebraic expression that represents the combined area, combine like terms. First, regroup the terms by using the associative and commutative properties of addition so our like terms are together.<\/p>\n<p class=\"longmath\" style=\"text-align: center;\">\\((16x^2+5x^2)+(48x-54x)+(36+40)\\)<\/p>\n<p>Now, simplify each group of like terms by combing them.<\/p>\n<p style=\"text-align: center;\">\\(21x^2+(-6x)+76\\)<\/p>\n<p>Lastly, simplify adding \\(+(-6x)\\) to \\(-6x\\).<\/p>\n<p style=\"text-align: center;\">\\(21x^2-6x+76\\)<\/p>\n<p>Since there are no more like terms to combine, the expression for the combined area is completely simplified, so the combined area is \\(21x^2-6x+76\\) square feet.<\/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>&nbsp;<br \/>\nOn the first day of a sale, the profit generated, in dollars, of selling a new brand of an exterior paint is represented by the algebraic expression \\(2x+5xy+9y\\). On the second day of the sale, the profit generated for selling the same paint is represented by the algebraic expression \\(x+7xy-2y\\). Which of the following algebraic expressions represents is the difference in profit from the first day of the sale to the second day?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(3x-12xy-7y\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(x+2xy+11y\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(x-2xy+11y\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(3x-2xy+11y\\)<\/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 difference in profit from the first and second day of the sale, we must take the difference in the two expressions representing the profits from the respective days.<\/p>\n<p style=\"text-align: center;\">\\((2x+5xy+9y)\\)\\(-(x+7xy-2y)\\)<\/p>\n<p>To simplify an algebraic expression, we want to combine like terms. <\/p>\n<p>Before combining like terms, we can change the subtraction sign between the two expressions to an addition sign by \u201cadding the negative of it\u201d.<\/p>\n<p style=\"text-align: center;\">\\((2x+5xy+9y)\\)\\(+(-1)(x+7xy-2y)\\)<\/p>\n<p>The \u22121 gets distributed to the second expression to give us:<\/p>\n<p style=\"text-align: center;\">\\((2x+5xy+9y)\\)\\(+(-x-7xy+2y)\\)<\/p>\n<p>Now, regroup the terms by using the associative and commutative properties of addition so our like terms are together.<\/p>\n<p style=\"text-align: center;\">\\((2x-x)+(5xy-7xy)\\)\\(+(9y+2y)\\)<\/p>\n<p>Simplify each group of like terms by combing them.<\/p>\n<p style=\"text-align: center;\">\\(x+(-2xy)+11y\\)<\/p>\n<p>Lastly, simplify \\(+(-2xy)\\) to \\(-2xy\\).<\/p>\n<p style=\"text-align: center;\">\\(x-2xy+11y\\)<\/p>\n<p>There are no more like terms to combine, the expression is completely simplified, so the difference in the profit from the first day to the second day of the sale is \\(x-2xy+11y\\) dollars. <\/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":22,"featured_media":114725,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-114722","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-practice-question-videos","7":"page_type-video","8":"content_type-practice-questions","9":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/114722","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=114722"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/114722\/revisions"}],"predecessor-version":[{"id":281105,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/114722\/revisions\/281105"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/114725"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=114722"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}