Question

Factorize each of the following expression:
(x + 2y)² − 4(2x − y)²

Answer 1

$$\begin{gathered} (x+2y{)}^2-4(2x-y{)}^2=(x+2y{)}^2-[2(2x-y){]}^2 \\ =\left[\right(x+2y)-2(2x-y\left)\right]\left[\right(x+2y)+2(2x-y\left)\right] \\ =(x+2y-4x+2y)(x+2y+4x-2y) \\ =5x(4y-3x) \end{gathered}$$