SOLUTION: The product of (a + b)(a − b) is a perfect square trinomial? A: Sometimes B: Always C: Never isnt it always?

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Question 338082: The product of (a + b)(a − b) is a perfect square trinomial?
A: Sometimes
B: Always
C: Never
isnt it always?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

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