this week in math 10 I learned that if we have a binomial that says $x^2-81$ for example, this is considered a perfect square because $x^2$ = (x)(x) , 81= (9)(9). there is no middle term because when factored it would look like (x-9)(x+9), then if you were to expand this back out, the -9 and the +9 would cancel out and become 0, leaving the answer to be a binomial instead of a trinomial. (x)(x)= $x^2$ + (x)(9)= +9x (-9)(x) = -9x (-9)(9) = -81

$x^2$ + 9x – 9x -81 .    the +9x and the -9x cancel out to be zero

for this to be a “perfect square” we need to make sure that each term is a perfect square and that the sign is subtraction, not addition