Please show the mathematical solution and not the procedure.

<h2>Adding and Subtracting Polynomials</h2>
<p>Adding and subtracting polynomials can be thought of as just adding and subtracting like terms. Look for like terms—those with the same variables with the same exponent. The <strong>Commutative Property</strong> allows us to rearrange the terms to put like terms together. It may also be helpful to underline, circle, or box like terms.</p>
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<h2>Example</h2>
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<p>Find the sum: \(\left(4{x}^{2}-5x+1\right)+\left(3{x}^{2}-8x-9\right).\)</p>
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<h3>Solution</h3>
<table data-label="" style="width: 605px;" summary="The top row shows parentheses 4 x squared minus 5x plus 1 plus parentheses 3 x squared minus 8x minus 9. The next row says, “Identify like terms,” and 4 x squared and 3 x squared have double underlines, 5x and 8x are underlined, and 1 and 9 are in boxes. The next line says, “Rearrange to get the like terms together,” and shows 4 x squared plus 3 x squared minus 5x minus 8x plus 1 minus 9. The last step says, “Combine like terms,” and shows 7 x squared minus 13x minus 8.">
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<td style="width: 288px;"> </td>
<td style="width: 303px;"><img alt="." src="https://data.ulearngo.com/assets/a080e7f3-7d7c-422a-8e00-da988a1349e1"/></td>
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<td style="width: 288px;">Identify like terms.</td>
<td style="width: 303px;"><img alt="." src="https://data.ulearngo.com/assets/a96747be-7aa4-4363-8783-204cbf683410"/></td>
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<td style="width: 288px;">Rearrange to get the like terms together.</td>
<td style="width: 303px;"><img alt="." src="https://data.ulearngo.com/assets/eb656ada-9526-44fe-8884-5cd504b9eb5f"/></td>
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<td style="width: 288px;">Combine like terms.</td>
<td style="width: 303px;"><img alt="." src="https://data.ulearngo.com/assets/4acf1c1d-ffc3-4597-aec5-b25d2f3e1f54"/></td>
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</tbody>
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<p>Parentheses are grouping symbols. When we add polynomials as we did in the previous lesson, we can rewrite the expression without parentheses and then combine like terms. But when we subtract polynomials, we must be very careful with the signs.</p>
<h3>Optional Video: Adding Polynomials</h3>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="337" src="https://www.youtube.com/embed/KYZR7g7QcF4?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="599"></iframe></p>
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<h2>Example</h2>
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<p>Find the difference: \(\left(7{u}^{2}-5u+3\right)-\left(4{u}^{2}-2\right).\)</p>
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<h3>Solution</h3>
<table data-label="" style="width: 469px;" summary="The top row shows parentheses 7 u squared minus 5u plus 3 minus parentheses 4 u squared minus 2. The next line says, “Distribute and identify like terms,” and shows 7 u squared minus 5u plus 3 minus 4 u squared plus 2. The 7 u squared and 4 u squared have double underlines, 5u is underlined, and 3 and 2 are in boxes. The next line says, “Rearrange the terms,” and shows 7 u squared minus 4 u squared minus 5u plus 3 plus 2. The last line says, “Combine like terms,” and shows 3 u squared minus 5u plus 5.">
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<td style="width: 234px;"> </td>
<td style="width: 221px;"><img alt="." src="https://data.ulearngo.com/assets/74fdb11d-cf59-4b6e-8bff-33c172a3151d"/></td>
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<td style="width: 234px;">Distribute and identify like terms.</td>
<td style="width: 221px;"><img alt="." src="https://data.ulearngo.com/assets/2497534e-0d6c-460d-ad80-e633b51604e2"/></td>
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<td style="width: 234px;">Rearrange the terms.</td>
<td style="width: 221px;"><img alt="." src="https://data.ulearngo.com/assets/a77c1729-8dd6-4474-93fb-a22a99a8f594"/></td>
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<td style="width: 234px;">Combine like terms.</td>
<td style="width: 221px;"><img alt="." src="https://data.ulearngo.com/assets/c2bb24fd-41e7-4b3d-80f4-af8aa11bf10b"/></td>
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<h2>Example</h2>
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<p>Subtract: \(\left({m}^{2}-3m+8\right)\) from \(\left(9{m}^{2}-7m+4\right).\)</p>
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<h3>Solution</h3>
<table data-label="" style="width: 645px;" summary="The top line says, “Subtract parentheses m squared minus 3m plus 8 from parentheses 9 m squared minus 7m plus 4.” The next line says, “Distribute and identify like terms,” and shows 9 m squared minus 7m plus 4 minus m squared plus 3m minus 8. The 9 m squared and m squared are double underlined, 7m and 3m are underlined, and 4 and 8 are in boxes. The next line says, “Rearrange the terms,” and shows 9 m squared minus m squared minus 7m plus 3m plus 4 minus 8. The last step says, “Combine like terms,” and shows 8 m squared minus 4m minus 4.">
<tbody>
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<td style="width: 234px;"> </td>
<td style="width: 397px;"><img alt="." src="https://data.ulearngo.com/assets/3218e058-9b0d-4a3c-b915-0e0f6acbd5a1"/></td>
</tr>
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<td style="width: 234px;">Distribute and identify like terms.</td>
<td style="width: 397px;"><img alt="." src="https://data.ulearngo.com/assets/bed50b6e-0cc1-4ef6-9a25-b7f413e1a5b7"/></td>
</tr>
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<td style="width: 234px;">Rearrange the terms.</td>
<td style="width: 397px;"><img alt="." src="https://data.ulearngo.com/assets/496cafce-8bac-4031-b931-7438e2b8ba53"/></td>
</tr>
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<td style="width: 234px;">Combine like terms.</td>
<td style="width: 397px;"><img alt="." src="https://data.ulearngo.com/assets/a2c87beb-6661-4ab2-859e-80ac4deacb53"/></td>
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</tbody>
</table>
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<h3>Optional Video: Subtracting Polynomials</h3>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="337" src="https://www.youtube.com/embed/xq-zVm25VC0?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="599"><span class="mce_SELRES_start" data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;">﻿</span></iframe></p>

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Adding and Subtracting Polynomials

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Discover how to identify, determine the degree of, add, subtract, multiply, divide, and factor polynomials while also simplifying expressions with exponents in this tutorial.


Adding and Subtracting Polynomials

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