Question

when you multiply a difference of two squares, why is your answer a binomial instead of a trinomial like when you multiply the sum of two squares

Answer 1

Difference of two squares:

(a+b)(a-b) = a² - b²
(a-b)(a+b) = a² - b²

The difference of two squares results to a binomial because the middle  term cancels each other out.

example:
a = 2 ; b = 3

(2 - 3)(2 + 3) = 2(2+3)-3(2+3) = 4+6-6+9 = 4 + 0 + 9 = 4 + 9