Factor 2(x-y)^2-3(x-y)^3

$2 {(x - y)}^{2} - 3 {(x - y)}^{3}$

Step 1

Factor ${(x - y)}^{2}$ out of $2 {(x - y)}^{2} - 3 {(x - y)}^{3}$ .

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

${(x - y)}^{2} \cdot 2 - 3 {(x - y)}^{3}$

Factor ${(x - y)}^{2}$ out of $- 3 {(x - y)}^{3}$ .

${(x - y)}^{2} \cdot 2 + {(x - y)}^{2} (- 3 (x - y))$

Factor ${(x - y)}^{2}$ out of ${(x - y)}^{2} \cdot 2 + {(x - y)}^{2} (- 3 (x - y))$ .

${(x - y)}^{2} (2 - 3 (x - y))$

Step 2

Apply the distributive property.

${(x - y)}^{2} (2 - 3 x - 3 (- y))$

Step 3

Multiply $- 1$ by $- 3$ .

${(x - y)}^{2} (2 - 3 x + 3 y)$

Step 4

Factor.

Factor $- 1$ out of $2 - 3 x + 3 y$ .

Move $2$ .

${(x - y)}^{2} (- 3 x + 3 y + 2)$

Factor $- 1$ out of $- 3 x$ .

${(x - y)}^{2} (- (3 x) + 3 y + 2)$

Factor $- 1$ out of $3 y$ .

${(x - y)}^{2} (- (3 x) - (- 3 y) + 2)$

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

${(x - y)}^{2} (- (3 x) - (- 3 y) - 1 (- 2))$

Factor $- 1$ out of $- (3 x) - (- 3 y)$ .

${(x - y)}^{2} (- (3 x - 3 y) - 1 (- 2))$

Factor $- 1$ out of $- (3 x - 3 y) - 1 (- 2)$ .

${(x - y)}^{2} (- (3 x - 3 y - 2))$

Remove unnecessary parentheses.

${(x - y)}^{2} \cdot - 1 (3 x - 3 y - 2)$

Step 5

Factor out negative.

$- ({(x - y)}^{2} (3 x - 3 y - 2))$

Step 6

Remove unnecessary parentheses.

$- {(x - y)}^{2} (3 x - 3 y - 2)$