document.write( "Question 88596: how can i factor x^2+4x+4-y^2 \n" ); document.write( "

Algebra.Com's Answer #64412 by bucky(2189) $\"\"$ $\"About$

You can put this solution on YOUR website!
Given:
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\n" ); document.write( " $\"x%5E2%2B4x%2B4-y%5E2\"$
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\n" ); document.write( "Let's set off the first part of this in parentheses as follows:
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\n" ); document.write( " $\"%28x%5E2%2B4x%2B4%29-y%5E2\"$
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\n" ); document.write( "Now notice that the terms in the parentheses are a perfect square. They are equal to $\"%28x%2B2%29%5E2\"$ .
\n" ); document.write( "Substituting this into the original polynomial results in:
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\n" ); document.write( " $\"%28x%2B2%29%5E2+-y%5E2\"$
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\n" ); document.write( "Now you have something of the form $\"a%5E2+-+b%5E2\"$ in which a = x+2 and b = y. And $\"a%5E2+-+b%5E2\"$
\n" ); document.write( "factors into $\"%28a%2Bb%29%2A%28a+-+b%29\"$
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\n" ); document.write( "Substituting (x+2) for \"a\" and y for \"b\" results in:
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\n" ); document.write( " $\"%28a%2Bb%29%2A%28a-b%29\"$
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\n" ); document.write( "becoming:
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\n" ); document.write( " $\"%28%28x%2B2%29%2By%29%2A%28%28x%2B2%29-y%29\"$
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\n" ); document.write( "and removing the parentheses around the (x + 2) terms gives the final answer of:
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\n" ); document.write( " $\"%28x%2B2%2By%29%2A%28x%2B2-y%29\"$
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\n" ); document.write( "Hope this helps you to understand the problem a little better. Cheers! \n" ); document.write( "

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