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181 lines
6.5 KiB
HTML
181 lines
6.5 KiB
HTML
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Like Terms</h1>
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<p class="center"><i>It may help you to read <a href="introduction.html">Introduction to Algebra</a> first</i></p>
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<h2>Like Terms</h2>
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<p>"Like terms" are <b>terms</b> whose variables (and their <a href="../exponent.html">exponents</a> such as the 2 in x<sup>2</sup>) are the same.</p>
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<p>In other words, terms that are "like" each other.</p>
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<p>Note: the <b>coefficients</b> (the numbers you multiply by, such as "5" in 5x) can be different.</p>
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<div class="example">
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<h3>Example:</h3>
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<div class="centerfull larger">
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<div class="boxa">7<b>x</b></div>
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<div class="boxa"><b>x</b></div>
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<div class="boxa">−2<b>x</b></div>
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</div>
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<p>Are all <b>like terms</b> because the variables are all <b>x</b></p>
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</div>
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<div class="example">
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<h3>Example:</h3>
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<div class="centerfull larger">
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<div class="boxa">(1/3)<b>xy<sup>2</sup></b></div>
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<div class="boxa">−2<b>xy<sup>2</sup></b></div>
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<div class="boxa">6<b>xy<sup>2</sup></b></div>
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<div class="boxa"><b>xy<sup>2</sup></b>/2</div>
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</div>
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<p>Are all <b>like terms</b> because the variables are all <b>xy<sup>2</sup></b></p>
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</div>
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<h2>Unlike Terms</h2>
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<p>If they are not like terms, they are called "<b>Unlike Terms</b>":</p>
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<div class="beach">
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<table align="center" width="80%" border="0">
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<tbody>
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<tr style="text-align:center;">
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<th colspan="3">Unlike Terms</th>
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<th>Why they are "Unlike Terms"</th>
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</tr>
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<tr style="text-align:center;">
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<td>−3xy</td>
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<td>−3y</td>
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<td>12y<sup>2</sup></td>
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<td><span class="times">←</span> these are all <b>unlike terms</b> <b><br>
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</b>(<b>xy</b>, <b>y</b> and <b>y<sup>2</sup></b> are all different)</td>
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</tr>
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</tbody></table>
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</div>
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<div class="example">
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<h3>Example: These are all <b>Unlike</b> Terms because the variables and/or their exponents are different:</h3>
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<div class="centerfull larger">
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<div class="boxa">2<b style="color:blue;">x</b></div>
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<div class="boxa">2<b style="color:red;">x<sup>2</sup></b></div>
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<div class="boxa">2<b style="color:green;">y</b></div>
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<div class="boxa">2<b style="color:orange;">xy</b></div>
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</div>
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<br>
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</div>
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<h2>Combining Like Terms</h2>
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<p>You can add <b>like terms</b> together to make one term:</p>
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<div class="example">
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<h3>Example: 7<b>x</b> + <b>x</b></h3>
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<p>They are both <b>like terms</b>, so you can just add them:</p>
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<p class="center larger">7<b>x</b> + <b>x</b> = 8<b>x</b></p>
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</div>
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<div class="center80">
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<h3>By the way ... why don't we write "1x" ?</h3>
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<p>It is simpler to write <b>x</b>, and is so common that "1x" looks strange.</p></div>
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<p> </p>
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<div class="example">
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<h3>Example: 4<b>x<sup>3</sup></b> + 3<b>x<sup>2</sup></b> − 7 − <b>x<sup>2</sup></b> + 2</h3>
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<p>Some of the terms are <b>like terms</b>.</p>
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<p>Combine <b>like terms</b>:</p>
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<p class="center">(4<b>x<sup>3</sup></b>) + (3<b>x<sup>2</sup></b> − <b>x<sup>2</sup></b>) + (2 − 7)</p>
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<p>Then add <b>like terms</b>:</p>
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<p class="center">4<b>x<sup>3</sup></b> + 2<b>x<sup>2</sup></b> − 5</p>
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</div>
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<p> </p>
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<div class="questions">
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<script>getQ(2051,2052,5498,5499,5500,2053,2054,5520,5521,5522);</script>
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</div>
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<div class="related">
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<a href="introduction.html">Introduction to Algebra</a>
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<a href="index.html">Algebra Index</a>
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