Question

Which products result in a difference of squares? Select three options.

(x minus y)(y minus x)
(6 minus y)(6 minus y)
(3 + x z)(negative 3 + x z)
(y squared minus x y)(y squared + x y)
(64 y squared + x squared)(negative x squared + 64 y squared)

Answer 1

The three that are differences of squares are:

- (3 + x z)(-3 + x z) = (xz + 3)(xz - 3) = (xz)^2 - 3^2
- (y^2 - x y)(y^2 + x y) = (y^2)^2 - (xy)^2
- (64 y^2 + x^2)(-x^2 + 64 y^2) = (64y^2 + x^2)(64y^2 - x^2) = (64y^2)^2 - (x^2)^2

(For completeness: (x - y)(y - x) = -(x - y)^2 and (6 - y)(6 - y) = (6 - y)^2, which are not in the standard (A + B)(A - B) difference-of-squares form.)