Factor -3b(b-2)+7(b-2)^2

$- 3 b (b - 2) + 7 {(b - 2)}^{2}$

Step 1

Factor $- (b - 2)$ out of $- 3 b (b - 2) + 7 {(b - 2)}^{2}$ .

Factor $- (b - 2)$ out of $- 3 b (b - 2)$ .

$- (b - 2) (3 b) + 7 {(b - 2)}^{2}$

Factor $- (b - 2)$ out of $7 {(b - 2)}^{2}$ .

$- (b - 2) (3 b) - (b - 2) (- 7 (b - 2))$

Factor $- (b - 2)$ out of $- (b - 2) (3 b) - (b - 2) (- 7 (b - 2))$ .

$- (b - 2) (3 b - 7 (b - 2))$

Step 2

Apply the distributive property.

$- (b - 2) (3 b - 7 b - 7 \cdot - 2)$

Step 3

Multiply $- 7$ by $- 2$ .

$- (b - 2) (3 b - 7 b + 14)$

Step 4

Subtract $7 b$ from $3 b$ .

$- (b - 2) (- 4 b + 14)$

Step 5

Factor.

Factor $2$ out of $- 4 b + 14$ .

Factor $2$ out of $- 4 b$ .

$- (b - 2) (2 (- 2 b) + 14)$

Factor $2$ out of $14$ .

$- (b - 2) (2 (- 2 b) + 2 (7))$

Factor $2$ out of $2 (- 2 b) + 2 (7)$ .

$- (b - 2) (2 (- 2 b + 7))$

Remove unnecessary parentheses.

$- (b - 2) \cdot 2 (- 2 b + 7)$

Step 6

Multiply $2$ by $- 1$ .

$- 2 (b - 2) (- 2 b + 7)$

Step 7

Factor.

Factor $- 1$ out of $- 2 b + 7$ .

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

$- 2 (b - 2) (- (2 b) + 7)$

Rewrite $7$ as $- 1 (- 7)$ .

$- 2 (b - 2) (- (2 b) - 1 (- 7))$

Factor $- 1$ out of $- (2 b) - 1 (- 7)$ .

$- 2 (b - 2) (- (2 b - 7))$

Remove unnecessary parentheses.

$- 2 (b - 2) \cdot - 1 (2 b - 7)$

Step 8

Combine exponents.

Factor out negative.

$- (- 2 (b - 2) (2 b - 7))$

Multiply $- 2$ by $- 1$ .

$2 ((b - 2) (2 b - 7))$

Step 9

Remove unnecessary parentheses.

$2 (b - 2) (2 b - 7)$

Factor -3b(b-2)+7(b-2)^2

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