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7a267684-30cc-4a01-8a4b-83c51f399d04.html
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<h4>Activity</h4>
<p>We will solve these two problems as a class.</p>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent">
<li>Do these terms have the same variables with the same exponents? Explain your answer. <br>
<br>
\(6x^4y^2\) \(8x^4y^2\) </li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answer:</p>
<p>Yes. Both terms have the same variables raised to the same degrees: \(x\) is raised to the fourth power, and \(y\) is squared.</p>
</div>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal2" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="2">
<li> Add the terms together: \(6x^4y^2+8x^4y^2\). What is the sum? <br>
</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal2">
<p>Compare your answer:</p>
<p>\(14x^4y^2\)</p>
</div>
<br>
<p>In problems 3 - 7, simplify the monomial addition and subtraction problems on your own. Write down your answer, then select the solution button to compare your work.</p>
<br>
<!--Q#3-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal3" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="3">
<li>\(12q+9q\)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal3" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(21q\)</p>
</div>
<!--Interaction End -->
<br>
<!--Q#4-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal4" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="4">
<li>\(-14c^3+5c^3\)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal4" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(-9c^3\)</p>
</div>
<!--Interaction End -->
<br>
<!--Q#5-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal5" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="5">
<li> \(8g^2h^2+(-6g^2h^2)\)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal5" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(2g^2h^2\)</p>
</div>
<!--Interaction End -->
<br>
<!--Q#6-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal6" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="6">
<li> \(8mn^3p-(-5mn^3p)\)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal6" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(13mn^3p\)</p>
</div>
<!--Interaction End -->
<br>
<!--Q#7-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal7" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="7">
<li> \(-16a^2+3b^2+8a^2 \)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal7" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(-8a^2+3b^2\)</p>
</div>
<!--Interaction End -->
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="52fdbc4d-81fd-4d07-a13e-40a06038bc34" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="8">
<li> Can the following monomials be simplified using like terms? Explain. <br>
<br>
\(17a^2bc^3+6a^2b^2c^3\) </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>No, the monomial terms do not contain the same variables with the same exponents. The first term has the variable \(b\) with an exponent of 1. The second term has the variable \(b\) with an exponent of 2. The monomials are not like terms.</p>
</div>
</div>
<br>
<p>In problems 9 - 13, simplify the polynomial addition and subtraction problems on your own. Write down your answer, then select the solution button to compare your work.</p>
<br>
<!--Q#9-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal9" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="9">
<li>\( (5k+7m-2)+(7k+9m-4)\)</li>
</ol>
<p>You can use the following video if you need some help.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container">
<video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/ba5bc330fb9f7f706e35cf5a38cdfedb85f34aec">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/712187a19365bfc0825bd798bf9f258c6ec2c971" srclang="en_us">
</video>
</div>
</div>
<br>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal9" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(12k+16m-6\)</p>
</div>
<!--Interaction End -->
<br>
<!--Q#10-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal10" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="10">
<li>\((12w-11)-(5w+6) \)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal10" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(7w-5\)</p>
</div>
<!--Interaction End -->
<br>
<!--Q#11-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal11" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="11">
<li>\((9h^2-4h+17)+(2h^2-9)\)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal11" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(11h^2-4h+8\)</p>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#12-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal12" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="12">
<li> \((8f^2+6fv-3v^2)-(6f^2-3v^2)\)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal12" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(2f^2+6fv\)</p>
</div>
<!--Interaction End -->
<br>
<!--Q#13-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal13" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="13">
<li> \((8z^3-6zx+3x^2)+(12z^3-4zx)\)</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-wait-for-event="Reveal13" data-schema-version="1.0">
<p>Compare your answer:</p>
<p>\(20z^3-10zx+3x^2\)</p>
</div>
<!--Interaction End -->
<br>
<!-- "Start "Are you Ready for More? click to reveal. If you have more than one on a page, you will need to change the Data-fire/data-wait-for-events for each set.-->
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<!--Start interaction. If multiple interactions appear under "are you ready for more?, they should all have matching "data-wait-for-event", which should also match the "data-fire-event" for the button. Note in this sample, they are all RFM1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="3cd1023e-3b4a-4e82-b3b2-ddd9101db872" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>Simplify. Use the "^" symbol to enter an exponent.</p>
<p>\((6a^3-2a^2b)-2(ab^2+3b^3)+(2a^2b+2ab^2)\)</p>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(6a^3-6b^3\)</p>
<p>Here is how to solve this problem:<br>
\((6a^3-2a^2b)-2(ab^2+3b^3)+(2a^2b+2ab^2)\)</p>
<p><strong>Step 1 -
</strong>Distribute the multiplication over addition.</p>
<p> \(6a^3-2a^2b-2ab^2-6b^3+2a^2b+2ab^2\)</p>
<p><strong>Step 2 -
</strong>Use the Commutative Property to rearrange like terms together.</p>
<p> \(6a^3-2a^2b+2a^2b-2ab^2+2ab^2-6b^3\)</p>
<p><strong>Step 3 -
</strong>Combine like terms.</p>
<p> \(6a^3-6b^3\)</p>
</div>
</div>
<!--End interaction-->