Question 338082
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No, for to be a perfect square it must be the product of two identical factors.
(a+b) and (a-b) are NOT necessarily identical at all.  There are cases when
it would in the end turn out to be the product of two identical factors.  For
instance if a=5 and b=3, then

(a+b)(a-b) = (5+3)(5-3) = (8)(2) = 16 and 16 is 4×4 or the perfect 
square 4².

Also it will be a perfect square if b=0 because

(a+b)(a-b) = (a+0)(a-0) = (a)(a) = a², which is a perfect square, 

But in general it is not necessarily a perfect square. So the correct answer
is "sometimes".

Edwin</font>