<s>[INST] Factor the Expression completely$ (a+b)^2 - (a-b)^2$ I don't understand this question. The answer in the book is $4ab$, but how is that term a factor?
I was thinking along the line that this was a difference of squares example. $a^2-b^2 = (a+b)(a-b)$
My answer is $[(a+b)-(a-b)][(a+b)+(a-b)]$
What do I not understand?  
 [/INST] Just See this,
$(a+b)^2 = a^2 + b^2 +2ab$,
$(a-b)^2 = a^2 + b^2 -2ab$
Subtract them,
 You will get $4ab$
Ok I will show that , you have already done everything
$(a+b)^2 - (a-b)^2 = [(a+b)-(a-b)][(a+b)+(a-b)]$
$\hspace{2cm} = [a+b-a+b][a+b+a-b]$
$\hspace{2cm} = [a-a+b+b][a+a+b-b]$
$\hspace{2cm} = [2b][2a]$
$\hspace{2cm} = 4ab$
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