Factor 2(x-2)(x+1)^2-3(x-2)^2(x+1)

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

Factor $(x - 2) (x + 1)$ out of $2 (x - 2) {(x + 1)}^{2} - 3 {(x - 2)}^{2} (x + 1)$ .

Factor $(x - 2) (x + 1)$ out of $2 (x - 2) {(x + 1)}^{2}$ .

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

Factor $(x - 2) (x + 1)$ out of $- 3 {(x - 2)}^{2} (x + 1)$ .

$(x - 2) (x + 1) (2 (x + 1)) + (x - 2) (x + 1) (- 3 (x - 2))$

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

$(x - 2) (x + 1) (2 (x + 1) - 3 (x - 2))$

Apply the distributive property.

$(x - 2) (x + 1) (2 x + 2 \cdot 1 - 3 (x - 2))$

Multiply $2$ by $1$ .

$(x - 2) (x + 1) (2 x + 2 - 3 (x - 2))$

Apply the distributive property.

$(x - 2) (x + 1) (2 x + 2 - 3 x - 3 \cdot - 2)$

Multiply $- 3$ by $- 2$ .

$(x - 2) (x + 1) (2 x + 2 - 3 x + 6)$

Subtract $3 x$ from $2 x$ .

$(x - 2) (x + 1) (- x + 2 + 6)$

Add $2$ and $6$ .

$(x - 2) (x + 1) (- x + 8)$

Factor.

Factor $- 1$ out of $- x + 8$ .

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

$(x - 2) (x + 1) (- (x) + 8)$

Rewrite $8$ as $- 1 (- 8)$ .

$(x - 2) (x + 1) (- (x) - 1 (- 8))$

Factor $- 1$ out of $- (x) - 1 (- 8)$ .

$(x - 2) (x + 1) (- (x - 8))$

Remove unnecessary parentheses.

$(x - 2) (x + 1) \cdot - 1 (x - 8)$

Factor out negative.

$- ((x - 2) (x + 1) (x - 8))$

Remove unnecessary parentheses.

$- (x - 2) (x + 1) (x - 8)$