Simplify 2(3-b)+5(b-3)^2

$2 (3 - b) + 5 {(b - 3)}^{2}$

Simplify each term.

Apply the distributive property.

$2 \cdot 3 + 2 (- b) + 5 {(b - 3)}^{2}$

Multiply $2$ by $3$ .

$6 + 2 (- b) + 5 {(b - 3)}^{2}$

Multiply $- 1$ by $2$ .

$6 - 2 b + 5 {(b - 3)}^{2}$

Rewrite ${(b - 3)}^{2}$ as $(b - 3) (b - 3)$ .

$6 - 2 b + 5 ((b - 3) (b - 3))$

Expand $(b - 3) (b - 3)$ using the FOIL Method.

Apply the distributive property.

$6 - 2 b + 5 (b (b - 3) - 3 (b - 3))$

Apply the distributive property.

$6 - 2 b + 5 (b \cdot b + b \cdot - 3 - 3 (b - 3))$

Apply the distributive property.

$6 - 2 b + 5 (b \cdot b + b \cdot - 3 - 3 b - 3 \cdot - 3)$

Simplify and combine like terms.

Simplify each term.

Multiply $b$ by $b$ .

$6 - 2 b + 5 (b^{2} + b \cdot - 3 - 3 b - 3 \cdot - 3)$

Move $- 3$ to the left of $b$ .

$6 - 2 b + 5 (b^{2} - 3 \cdot b - 3 b - 3 \cdot - 3)$

Multiply $- 3$ by $- 3$ .

$6 - 2 b + 5 (b^{2} - 3 b - 3 b + 9)$

Subtract $3 b$ from $- 3 b$ .

$6 - 2 b + 5 (b^{2} - 6 b + 9)$

Apply the distributive property.

$6 - 2 b + 5 b^{2} + 5 (- 6 b) + 5 \cdot 9$

Simplify.

Multiply $- 6$ by $5$ .

$6 - 2 b + 5 b^{2} - 30 b + 5 \cdot 9$

Multiply $5$ by $9$ .

$6 - 2 b + 5 b^{2} - 30 b + 45$

Simplify by adding terms.

Add $6$ and $45$ .

$- 2 b + 5 b^{2} - 30 b + 51$

Subtract $30 b$ from $- 2 b$ .

$5 b^{2} - 32 b + 51$