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

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

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

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

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

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

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

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

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

Apply the distributive property.

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

Multiply $- - y$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $y$ by $1$ .

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

Factor.

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

Move $2$ .

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

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

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

Factor $- 1$ out of $y$ .

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

Rewrite $2$ as $- 1 (- 2)$ .

$2 (x - y) (- (x) - 1 (- y) - 1 (- 2))$

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

$2 (x - y) (- (x - y) - 1 (- 2))$

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

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

Remove unnecessary parentheses.

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

Combine exponents.

Factor out negative.

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

Multiply $2$ by $- 1$ .

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

Remove unnecessary parentheses.

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