When you multiply a difference of two squares (a+b)(a-b), why is your answer a binomial instead of a trinomial like when you multiply the sum of two squares (a+b)(a+b)?
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You get a binomial in both cases.
Multiplying a difference of squares:
a(x2 - y2) = ax2 - ay2
Multiplying a sum of squares:
a(x2 + y2) = ax2 + ay2
There is no trinomial here.
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