Question

How would you factor

(x+y)^2-(x-y)^2

Answer 1

recall the difference of squares:

a^2 - b^2 = (a+b)(a-b)

this has the same pattern
(x+y)^2-(x-y)^2
= (x+y + x-y)(x+y - (x-y))
= 2x(2y)
= 4xy

or you could just expand the original ...
(x+y)^2-(x-y)^2
= x^2 + 2xy + y^2 - (x^2 - 2xy + y^2)
= 4xy