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1c4f0bda-226a-4b4d-bfca-eee40dec1922.html
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<h4>Activity</h4>
<p>The binomials in the expression \((x-7)(2x+4)\) are solved three different ways in the table. Describe how the two binomials are being multiplied. Use the "^" symbol to enter an exponent.</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">
<table class="os-raise-wideequaltable">
<thead>
<tr>
<th scope="col">Solution</th>
<th scope="col">Description of Solution.</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>\((x-7)(2x+4)\)</p>
<p>\(x(2x+4)-7(2x+4)\)</p>
<p>\(2x^2+4x-14x-28\)</p>
<p>\(2x^2-10x-28\)</p>
</td>
<td>
<p><strong>First,</strong> ______________________</p>
<p><strong>Second,</strong> ___________________</p>
<p><strong>Next,</strong> ___________________</p>
<p>So, the solution is \(2x^2-10x-28\).</p>
</td>
</tr>
<tr>
<td>
<p>
\(\begin{align*}
x &- 7 \\
\underline{\times \;\;\;\;\;\;\;\;\;\;2x}&\underline{~+ 4\;\;\;} \\
4x &- 28\\
\underline{2x^2 -14x} & \underline{\;\;\;\;\;\;\;\;\;}\\
2x^2 - 10x &-28 \\
\end{align*}\)
</p>
</td>
<td>
<p><strong>First,</strong> ______________________</p>
<p><strong>Second,</strong> ___________________</p>
<p><strong>Third,</strong> ____________________</p>
<p><strong>Next,</strong> ___________________</p>
<p>So, the solution is \(2x^2-10x-28\).</p>
</td>
</tr>
<tr>
<td>
<p><img alt="IMAGE SHOWING MULTIPLICATION OF THE BINOMIALS, WITH AN ARROW GOING FROM X TO 2X, AN ARROW GOING FROM X TO 4, AN ARROW GOING FROM NEGATIVE 7 TO 2X, AND AN ARROW GOING FROM NEGATIVE 7 TO 4." height="48" src="https://k12.openstax.org/contents/raise/resources/17c1f054ecdff8655d1c4473c0338a841a486bcc" width="91"></p>
<p>\(2x^2+4x-14x-28\)</p>
<p>\(2x^2-10x-28\)</p>
</td>
<td>
<p><strong>First,</strong> ______________________</p>
<p><strong>Second,</strong> ___________________</p>
<p><strong>Third,</strong> ____________________</p>
<p><strong>Next,</strong> ___________________</p>
<p>Combine like terms, and the solution is <span>\(2x^2-10x-28\).</span></p>
</td>
</tr>
</tbody>
</table>
<br>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answers, then discuss your steps with a partner. Do you agree on all of the steps? If not, make changes where needed.</p>
<p>When you have finished, 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 answers:</p>
<table class="os-raise-wideequaltable">
<thead>
<tr>
<th scope="col">Solution</th>
<th scope="col">Description of Solution.</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>\((x-7)(2x+4)\)</p>
<p>\(x(2x+4)-7(2x+4)\)</p>
<p>\(2x^2+4x-14x-28\)</p>
<p>\(2x^2-10x-28\)</p>
</td>
<td>
<p><strong>First</strong>, the second binomial \((2x + 4)\) is distributed to both of the terms in the first binomial.</p>
<p><strong>Second</strong>, individual terms are distributed.</p>
<p><strong>Next</strong>, the like terms \(4x\) and \(–14x\) are combined.</p>
<p>So, the solution is \(2x^2-10x-28\).</p>
</td>
</tr>
<tr>
<td>
<p>
\(\begin{align*}
x &- 7 \\
\underline{\times \;\;\;\;\;\;\;\;\;\;2x}&\underline{~+ 4\;\;\;} \\
4x &- 28\\
\underline{2x^2 -14x} & \underline{\;\;\;\;\;\;\;\;\;}\\
2x^2 - 10x &-28 \\
\end{align*}\)
</p>
</td>
<td>
<p><strong>First</strong>, the binomials are written vertically.</p>
<p><strong>Second</strong>, the last term of the bottom binomial is multiplied, or distributed, to each of the terms in the top binomial.</p>
<p><strong>Third</strong>, the first term of the bottom binomial is multiplied, or distributed, to each of the terms in the top binomial, being sure to line up the like terms vertically.</p>
<p><strong>Next</strong>, add the like terms. They should be “stacked” on top of each other.</p>
<p>So, the solution is \(2x^2-10x-28\).</p>
</td>
</tr>
<tr>
<td>
<p><img alt="IMAGE SHOWING MULTIPLICATION OF THE BINOMIALS, WITH AN ARROW GOING FROM X TO 2X, AN ARROW GOING FROM X TO 4, AN ARROW GOING FROM NEGATIVE 7 TO 2X, AND AN ARROW GOING FROM NEGATIVE 7 TO 4." height="48" src="https://k12.openstax.org/contents/raise/resources/17c1f054ecdff8655d1c4473c0338a841a486bcc" width="91"></p>
<p>\(2x^2+4x-14x-28\)</p>
<p>\(2x^2-10x-28\)</p>
</td>
<td>
<p><strong>First</strong>, distribute the first term of the front binomial to the first term of the back binomial (F).</p>
<p><strong>Second</strong>, distribute the first term of the front binomial to the second term of the back binomial (O).</p>
<p><strong>Third</strong>, distribute the second term of the front binomial to the first term of the back binomial (I).</p>
<p><strong>Next</strong>, distribute the second term of the front binomial to the second term of the back binomial (L).</p>
<p>Combine like terms, and the solution is \(2x^2-10x-28\).</p>
</td>
</tr>
</tbody>
</table>
<br>
</div>
<p>The video below can also help break down solutions if you find yourself stuck.</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/f7497b4b5abbe1e66c6824a9d34edeed4d604ee4">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/51d0d48cbf3748fea9b3f4ced85739724b6e9f84" srclang="en_us">
</video></div>
</div>
<br>
<br>
<p>Multiply each binomial. Use the "^" symbol to enter an exponent.</p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5df9e94c-10f3-4739-a813-1b8ace3be304" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li> \((a+6)(a-4)\) </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>\(a^2+2a-24\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="58ea57a5-6491-4595-8caa-8177b5aca968" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> \((5b+9)(4b+3)\) </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>\(20b^2+51b+27\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a272f1a0-dbe4-4e84-a857-9fabc6d579b7" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> \((5x^2-1)(2x-8)\) </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>\(10x^3-40x^2-2x+8\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="29409c56-699d-4c02-a967-54ed56eb9b27" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li> \((7mn+1)(11mn-3)\) </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>\(77m^2n^2-10mn-3\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<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="b3225cde-3a8e-4725-afa9-5d1f04ff3931" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>Multiply each binomial. Add like terms to simplify the expression. Use the "^" symbol to enter an exponent.</p>
<p>\((5x^2y-xy)(3x+y)+(6x+4y)(-3x^2y+2xy)\)</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>\((5x^2y-xy)(3x+y)+(6x+4y)(-3x^2y+2xy)\)</p>
<p>\(\;\;\;\;\;\;\;\;=15x^3y+5x^2y^2-3x^2y-xy^2-18x^3y+12x^2y-12x^2y^2+8xy^2\) </p>
<p>\(\;\;\;\;\;\;\;\;=-3x^3y+9x^2y-7x^2y^2+7xy^2\)</p>
</div>
</div>
<!--End interaction-->