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

Algebra.Com
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)   (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 44 or the perfect
square 4.
Also it will be a perfect square if b=0 because
(a+b)(a-b) = (a+0)(a-0) = (a)(a) = a, which is a perfect square,
But in general it is not necessarily a perfect square. So the correct answer
is "sometimes".
Edwin

RELATED QUESTIONS

a-(b-c)=a-b+c is it sometimes, always or never... (answered by stanbon)
Is it always true, sometimes true, or never true that the centroid is outside its... (answered by Alan3354)
The centroid of a triangle is ____?____ the circumcenter of a triangle. A. Always B.... (answered by richard1234)
The inverse of the function y = x2 is still a function. a) always b) sometimes c)... (answered by Fombitz,Theo)
A rational number is ___always____a real number a. always b. sometimes c.... (answered by solver91311,ramizjawadi,136493)
Consider the statement, “If a parallelogram is a square, then it is a rhombus.” A) (answered by MathLover1)
three points are ____ connected by one line a. never b. sometimes c.... (answered by solver91311)
Lines that are skew _____ intersect. a. always b. never c.... (answered by veronica1289)
Two skew lines are _____ parallel. a. always b. never c.... (answered by veronica1289)