Question 88596
Given:
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{{{x^2+4x+4-y^2}}}
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Let's set off the first part of this in parentheses as follows:
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{{{(x^2+4x+4)-y^2}}}
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Now notice that the terms in the parentheses are a perfect square. They are equal to {{{(x+2)^2}}}.
Substituting this into the original polynomial results in:
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{{{(x+2)^2 -y^2}}}
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Now you have something of the form {{{a^2 - b^2}}} in which a = x+2 and b = y. And  {{{a^2 - b^2}}}
factors into {{{(a+b)*(a - b)}}}
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Substituting (x+2) for "a" and y for "b" results in:
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{{{(a+b)*(a-b)}}}
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becoming:
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{{{((x+2)+y)*((x+2)-y)}}}
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and removing the parentheses around the (x + 2) terms gives the final answer of:
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{{{(x+2+y)*(x+2-y)}}}
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Hope this helps you to understand the problem a little better. Cheers!