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131 lines
6.3 KiB
HTML
131 lines
6.3 KiB
HTML
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<title>Polynomials - Long Multiplication</title>
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<h1 align="center">Polynomials - Long Multiplication</h1>
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<p><span class="larger">A polynomial looks like this:</span> </p>
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<div class="beach">
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<table border="0" align="center" cellpadding="5">
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<tr align="center">
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<td><img src="images/polynomial-example.svg" alt="polynomial example" /></td>
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</tr>
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<tr align="center">
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<td>example of a polynomial<br />
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this one has 3 terms</td>
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</tr>
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</table>
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</div>
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<p>We can multiply small polynomials using the method shown on <a href="polynomials-multiplying.html">Multiplying Polynomials</a></p>
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<p>But when the polynomials have 3 or more terms it is often easier (and less likely to have a mistake) when we use a method similar to <a href="../numbers/multiplication-long.html">Long Multiplication for Numbers</a> (please read that page first).</p>
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<h2>The Method</h2>
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<p>Choose one polynomial (the longest is a good choice) and then:</p>
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<ul>
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<li>multiply it by <b>the first term</b> of the other polynomial, writing the result down</li>
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<li>then multiply it by <b>the second term</b> of the other polynomial, writing the result under the matching terms from the first multiplication</li>
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<li>then multiply it by <b>the third term</b> of the other polynomial (if any) etc ...</li>
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<li>lastly, add up the columns.</li>
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</ul>
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<p>Laying the work out neatly in columns is the key, like this:</p>
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<script type="text/javascript">playerMain("images/polynomials-multiply-long-a.txt",600,300);</script>
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<p align="center"><i>(I wrote column headings of x, x<sup>2</sup> and x<sup>3</sup>, but you don't have to)</i></p>
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<p>By <b>lining up the columns</b>, and being careful to <b>put the terms under the correct columns</b>, the job becomes "automatic", and we can easily look back to see if we got it right, too.</p>
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<p> </p>
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<p>But what happens if a polynomial is missing, say, an <b>x</b> term or an <b>x<sup>2</sup></b> term? Just leave that column blank!</p>
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<p>Here is a more complicated example, with blank gaps:</p>
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<script type="text/javascript">playerMain("images/polynomials-multiply-long-b.txt",600,310);</script>
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<h2>More than One Variable</h2>
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<p>So far we have been multiplying polynomials with only one variable (<b>x</b>), but how do we handle polynomials with two or more variables (such as <b>x</b> and <b>y</b>)? What are the column headings?</p>
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<p>Just ignore the columns in the question, write down the answers as they come, <b>always checking</b> to see if we could put an answer under a matching answer:</p>
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<script type="text/javascript">playerMain("images/polynomials-multiply-long-c.txt",600,300);</script>
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<p> </p>
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<script type="text/javascript">getQ(348, 349, 2415, 2416, 3217, 3218, 3219, 3887, 3888, 3889);</script>
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<div class="related">
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<a href="polynomials.html">Polynomials</a>
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<a href="introduction.html">Introduction to Algebra</a>
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<a href="definitions.html">Algebra - Basic Definitions</a>
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<a href="index.html">Algebra Index</a> </div>
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Copyright © 2018 MathsIsFun.com
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