Factor 2(x-2y)^2-4x(x-2y)

$2 {(x - 2 y)}^{2} - 4 x (x - 2 y)$

Factor $2 (x - 2 y)$ out of $2 {(x - 2 y)}^{2} - 4 x (x - 2 y)$ .

Factor $2 (x - 2 y)$ out of $2 {(x - 2 y)}^{2}$ .

$2 (x - 2 y) (x - 2 y) - 4 x (x - 2 y)$

Factor $2 (x - 2 y)$ out of $- 4 x (x - 2 y)$ .

$2 (x - 2 y) (x - 2 y) + 2 (x - 2 y) (- 2 x)$

Factor $2 (x - 2 y)$ out of $2 (x - 2 y) (x - 2 y) + 2 (x - 2 y) (- 2 x)$ .

$2 (x - 2 y) (x - 2 y - 2 x)$

Subtract $2 x$ from $x$ .

$2 (x - 2 y) (- x - 2 y)$

Factor.

Factor $- 1$ out of $- x - 2 y$ .

Factor $- 1$ out of $- x$ .

$2 (x - 2 y) (- (x) - 2 y)$

Factor $- 1$ out of $- 2 y$ .

$2 (x - 2 y) (- (x) - (2 y))$

Factor $- 1$ out of $- (x) - (2 y)$ .

$2 (x - 2 y) (- (x + 2 y))$

Remove unnecessary parentheses.

$2 (x - 2 y) \cdot - 1 (x + 2 y)$

Combine exponents.

Factor out negative.

$- (2 (x - 2 y) (x + 2 y))$

Multiply $2$ by $- 1$ .

$- 2 ((x - 2 y) (x + 2 y))$

Remove unnecessary parentheses.

$- 2 (x - 2 y) (x + 2 y)$