What does difference of perfect squares mean in math?

Answer 1

Given two integers, x and y, their squares are x^2 and y^2.

The difference between them is called the difference of perfect squares and is (x^2-y^2)

This is important because we can always factor this as (x+y)(x-y).

We don't really need x and y to be integers, but in elementary algebra classes they often are. In reality, they can by any numbers.

The idea behind this is when you multiply (x+y)(x-y) the xy and -xy terms cancel each other out and you are left with the x^2 and -y^2 terms.