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<h4>Multiplying Binomials</h4>
<p>You can multiply polynomials using the distributive property.</p>
<p><strong>Example 1</strong></p>
<p>Multiply \((x+3)(x+7)\) using the distributive property.</p>
<p><strong>Step 1</strong> - Multiply each term in the first binomial by the second binomial.<br>
\((x+3)(x+7)\)<br>
\(x(x+7)+3(x+7)\)</p>
<p><strong>Step 2</strong> - Use the distributive property to eliminate the parentheses.<br>
\( x^2+7x+3x+21\)</p>
<p><strong>Step 3</strong> - Combine like terms.<br>
\(x^2+10x+21\)</p>
<p>There is a pattern when multiplying two polynomials that are binomials.</p>
<ul>
<li> The first term in the result is the product of the first terms in each binomial. </li>
<li> The second and third terms are the product of multiplying the two outer terms and then the two inner terms. </li>
<li> The last term results from multiplying the two last terms. </li>
</ul>
<p>The method “First, Outer, Inner, Last” is abreviated as FOIL. It represents multiplying the First terms, Last terms, Inner terms, and Last terms of the binomials. The word “FOIL” is easy to remember and ensures you find all four products.</p>
<p><strong>Example 2</strong></p>
<p>Multiply \((x+3)(x+7)\) using FOIL.</p>
<p><strong>Step 1</strong> - Multiply the First terms, Outer terms, Inner terms, and Last terms.</p>
<p><img alt="IMAGE SHOWING MULTIPLICATION OF THE BINOMIALS, WITH AN ARROW ABOVE GOING FROM X TO X labeled F, , AN ARROW BELOW GOING FROM X TO 7 labeled O, AN ARROW BELOW GOING FROM 3 TO X labeled I, AND AN ARROW ABOVE GOING FROM 3 to 7 labeled L." class="img-fluid atto_image_button_text-bottom" height="154" src="https://k12.openstax.org/contents/raise/resources/54d45079ab66474b35e53023eab28376a88b3543" width="159"></p>
<p>\(x^2+7x+3x+21\)</p>
<p><strong>Step 2</strong> - Combine like terms.<br>
\(x^2+10x+21\)</p>
<p><strong>Example 3</strong></p>
<p>Multiply \((x-3)(2x+7)\) using FOIL.</p>
<p><strong>Step 1</strong> - Multiply the First terms, Outer terms, Inner terms, and Last terms.<br>
\(2x^2+7x-6x-21\)</p>
<p><strong>Step 2</strong> - Combine like terms.<br>
\(2x^2+x-21\)</p>
<h4>Try It: Multiplying Binomials</h4>
<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">
<p>Multiply \((7x+1)(2x-3)\) using FOIL.</p>
</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><span>Here is how to multiply (7x+1)(2x-3) using FOIL.</span><br></p>
<p>Step 1</p>
<p>Multiply the First terms, Outer terms, Inner terms, and Last terms.</p>
<p>14x^2-21x+2x-3</p>
<p>Step 2</p>
<p>Combine like terms.</p>
<p>14x^2-19x-3</p>
</div>
<br>
<h4>Check Your Understanding</h4>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="2dea16b7-c046-49c2-82bb-58c84f9c23be" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#-->
<div class="os-raise-ib-pset-problem" data-content-id="a2ec34f1-a0ab-400f-99ba-a63e7f75839a" data-problem-type="multiplechoice" data-solution="\(6x^2+11x-10\)" data-solution-options='["\\(6x^2+11x-10\\)", "\\(6x^2-11x-10\\)", "\\(6x^2+15x-10\\)", "\\(6x^2+19x-10\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>Multiply the binomials.</p>
<p>\((2x+5)(3x-2)\)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Try again. Take a moment to think about what you learned in the mini-lesson review. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(6x^2+11x-10\). </p>
</div>
</div>
<!--END QUESTION.-->
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<div class="os-raise-ib-pset-correct-response">
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</div>
<div class="os-raise-ib-pset-encourage-response">
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</div>
</div>
<h4>Videos</h4>
<p>Watch the following video to learn more about multiplying binomials.</p>
<p><strong>Khan Academy: Multiplying Binomials</strong></p>
<br>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/ZMLFfTX615w;&rel=0" title="Example 1: Multiplying a binomial by a binomial | Algebra I | Khan Academy"></iframe></div>
</div>