SOLUTION: how can i factor x^2+4x+4-y^2

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Question 88596: how can i factor x^2+4x+4-y^2
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
.
x%5E2%2B4x%2B4-y%5E2
.
Let's set off the first part of this in parentheses as follows:
.
%28x%5E2%2B4x%2B4%29-y%5E2
.
Now notice that the terms in the parentheses are a perfect square. They are equal to %28x%2B2%29%5E2.
Substituting this into the original polynomial results in:
.
%28x%2B2%29%5E2+-y%5E2
.
Now you have something of the form a%5E2+-+b%5E2 in which a = x+2 and b = y. And a%5E2+-+b%5E2
factors into %28a%2Bb%29%2A%28a+-+b%29
.
Substituting (x+2) for "a" and y for "b" results in:
.
%28a%2Bb%29%2A%28a-b%29
.
becoming:
.
%28%28x%2B2%29%2By%29%2A%28%28x%2B2%29-y%29
.
and removing the parentheses around the (x + 2) terms gives the final answer of:
.
%28x%2B2%2By%29%2A%28x%2B2-y%29
.
Hope this helps you to understand the problem a little better. Cheers!