document.write( "Question 94957: Factor the expression.
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Algebra.Com's Answer #69145 by bucky(2189) $\"\"$ $\"About$

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Given:
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\n" ); document.write( " $\"a%5E2%28b-c%29+-+16b%5E2%28b+-c%29\"$
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\n" ); document.write( "Note that (b - c) is a factor that is common to the two terms you were given. Therefore,
\n" ); document.write( "it can be factored out of each term to give:
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\n" ); document.write( " $\"%28b-c%29%28a%5E2+-+16b%5E2%29\"$ <=== remember this step. We'll come back to it.
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\n" ); document.write( "Notice that the factor $\"a%5E2+-+16b%5E2\"$ is the difference of two squares. It is of the
\n" ); document.write( "form $\"%28%28a%29%5E2+-+%284b%29%5E2%29\"$ which can use the factoring rule for the difference of two
\n" ); document.write( "squares. This factoring rule says:
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\n" ); document.write( " $\"x%5E2+-+y%5E2+=+%28x+-+y%29%2A%28x+%2B+y%29\"$
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\n" ); document.write( "If you multiply out the right side of this rule, you will see that the product does equal
\n" ); document.write( "the left side. And by comparing this rule with the problem that we are working on, you
\n" ); document.write( "can see that x = a and y = 4b. So by substituting \"a\" for x and \"4b\" for y in the rule
\n" ); document.write( "you get that
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\n" ); document.write( " $\"a%5E2+-+%284b%29%5E2+=+%28a+-+4b%29%2A%28a+%2B+4b%29\"$
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\n" ); document.write( "Take the right side of this rule and substitute it for $\"a%5E2+-+16b%5E2\"$ in the expression
\n" ); document.write( "above that we wanted to remember. When you do that substitution you get:
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\n" ); document.write( " $\"%28b-c%29%28a%5E2+-+16b%5E2%29+=+%28b+-+c%29%28a+-+4b%29%2A%28a+%2B+4b%29\"$
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\n" ); document.write( "That's as far as we can go with the factoring. So the answer to the problem is:
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\n" ); document.write( " $\"%28b+-+c%29%28a+-+4b%29%2A%28a+%2B+4b%29\"$
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\n" ); document.write( "Hope that this helps you to understand the problem a little more and especially helps you
\n" ); document.write( "to use the factoring rule for the difference of two squares ... it turns out that this
\n" ); document.write( "is a fairly good rule to remember because it can be used quite often in factoring
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