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

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

Simplify each term.

Apply the distributive property.

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

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b$ .

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

Multiply $- 2$ by $- 3$ .

$- 3 b^{2} + 6 b + 7 {(b - 2)}^{2}$

Rewrite ${(b - 2)}^{2}$ as $(b - 2) (b - 2)$ .

$- 3 b^{2} + 6 b + 7 ((b - 2) (b - 2))$

Expand $(b - 2) (b - 2)$ using the FOIL Method.

Apply the distributive property.

$- 3 b^{2} + 6 b + 7 (b (b - 2) - 2 (b - 2))$

Apply the distributive property.

$- 3 b^{2} + 6 b + 7 (b \cdot b + b \cdot - 2 - 2 (b - 2))$

Apply the distributive property.

$- 3 b^{2} + 6 b + 7 (b \cdot b + b \cdot - 2 - 2 b - 2 \cdot - 2)$

Simplify and combine like terms.

Simplify each term.

Multiply $b$ by $b$ .

$- 3 b^{2} + 6 b + 7 (b^{2} + b \cdot - 2 - 2 b - 2 \cdot - 2)$

Move $- 2$ to the left of $b$ .

$- 3 b^{2} + 6 b + 7 (b^{2} - 2 \cdot b - 2 b - 2 \cdot - 2)$

Multiply $- 2$ by $- 2$ .

$- 3 b^{2} + 6 b + 7 (b^{2} - 2 b - 2 b + 4)$

Subtract $2 b$ from $- 2 b$ .

$- 3 b^{2} + 6 b + 7 (b^{2} - 4 b + 4)$

Apply the distributive property.

$- 3 b^{2} + 6 b + 7 b^{2} + 7 (- 4 b) + 7 \cdot 4$

Simplify.

Multiply $- 4$ by $7$ .

$- 3 b^{2} + 6 b + 7 b^{2} - 28 b + 7 \cdot 4$

Multiply $7$ by $4$ .

$- 3 b^{2} + 6 b + 7 b^{2} - 28 b + 28$

Simplify by adding terms.

Add $- 3 b^{2}$ and $7 b^{2}$ .

$4 b^{2} + 6 b - 28 b + 28$

Subtract $28 b$ from $6 b$ .

$4 b^{2} - 22 b + 28$