Question

Write as a product:

(2x+y)²–(x–2y)²

Answer 1

(2y - x )² = (x-2y)²

So x(2y - x )² + 2x²(x - 2y)

= x(x-2y)² + 2x²( x - 2y )

= x(x-2y)[(x-2y) + 2x]

= x(x-2y)(3x-2y)

please check for mistakes.

but this is the key idea: (2y-x)²=(x-2y)².