How do you factor $(a+b)^2-4b^2$ ?

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Answer 1 · 2016-01-04T14:43:56

Use the difference of squares identity to find:

$(a+b)^2-4b^2 = (a-b)(a+3b)$

The difference of squares identity can be written:

$A^2-B^2=(A-B)(A+B)$

Use this with $A=a+b$ and $B=2b$ as follows:

$(a+b)^2-4b^2$

$=(a+b)^2-(2b)^2$

$=((a+b)-2b)((a+b)+2b)$

$=(a-b)(a+3b)$

How do you factor (a+b)^2-4b^2(a+b)^2-4b^2?