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144 lines
6.3 KiB
HTML
144 lines
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HTML
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<!-- Mirrored from www.mathsisfun.com/algebra/expanding.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:48:22 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Algebra - Expanding</title>
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<meta name="description" content="Expanding means removing the ( ) but we have to do it the right way!">
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Algebra - Expanding</h1>
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<p align="center">"Expanding" means <b>removing the</b> <span class="large">( )</span> ... but we have to do it the right way!</p>
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<p><span class="large">( )</span> are called "parentheses" or "<a href="brackets.html">brackets</a>"</p>
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<div class="def">
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<p>Whatever is inside the <span class="large">( )</span> needs to be treated as a "package". </p>
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<p>So when multiplying: multiply by everything inside the "package".</p>
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</div><p> </p>
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<div class="example">
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<h3>Example: Expand 3 × (5+2)</h3>
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<p>Answer:</p>
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<p class="center"><img src="images/expanding-ex1.svg" alt="3 x (5+2) = 3 x 5 + 3 x 2"></p>
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<p>It is now expanded.</p>
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<p>We can also complete the calculation:</p>
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<p class="larger" align="center">3 × (5+2) = <b>3 × 5</b> + <b>3 × 2</b> <br>
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= 15 + 6 <br>
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= 21 </p>
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</div>
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<h2>In Algebra</h2>
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<p>In Algebra putting two things next to each other usually means to multiply. </p>
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<p align="center"> So <b>3(a+b)</b> means to multiply <b>3</b> by <b>(a+b)</b></p>
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<p>Here is an example of expanding, using variables <b>a</b>, <b>b</b> and <b>c</b> instead of numbers:</p>
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<script type="text/javascript">playerMain("images/expand-abc.txt",600,140);</script>
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<p>And here is another example involving some numbers. Notice the "·" between the 3 and 6 to mean multiply, so <b>3·6 = 18</b>:</p>
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<script type="text/javascript">playerMain("images/expand-3x6.txt",600,120);</script>
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<p><a href="../multiplying-negatives.html">Multiplying negatives</a> has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:</p>
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<script type="text/javascript">playerMain("images/expand-3am5.txt",600,120);</script>
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<p>In that case <b>−3 · -5 = +15</b> (a positive answer), but here is an example where the second part is negative:</p>
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<script type="text/javascript">playerMain("images/expand-2x-xa.txt",600,120);</script>
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<p>So the second term ended up negative because <b>2x · −a = −2ax</b>, (it is also neater to write "−2ax" rather than "−2xa").</p>
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<p> That was also interesting because of x being <a href="../square-root.html">squared</a> (x<sup>2</sup>)</p>
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<p>Lastly, we have an example with three terms inside:</p>
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<script type="text/javascript">playerMain("images/expand-a-2bc.txt",600,120);</script>
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<p>The same rule applies: multiply by everything inside the (). </p>
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<p>And here is a hint: when a multiplication is obvious (like <b>a · 2</b>) do it straight away, but when it needs more thought (like <b>a · −b</b>) leave it for the next line.</p>
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<h2>Many Times Many</h2>
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<p>How do we do something like this?</p>
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<p class="center larger">(x + 2y)(3x − 4y)</p>
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<p class="center">Read <a href="polynomials-multiplying.html">Multiplying Polynomials</a>to find out!</p>
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<h2>Conclusion</h2>
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<p>Multiply by everything inside the () </p>
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<p>Do it in two stages:</p>
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<ul>
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<li>Write down the multiplications</li>
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<li>Then do the multiplications </li>
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</ul>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(328, 329, 2096, 2097, 3166, 3167, 3168, 3169, 3874, 3875);</script>
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</div>
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<div class="related">
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<a href="index.html">Algebra Index</a></div>
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Copyright © 2018 MathsIsFun.com
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