Expand the Trigonometric Expression (b^2+4b+4)(-b+3)

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

Step 1

Expand $(b^{2} + 4 b + 4) (- b + 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $b^{2}$ by $b$ by adding the exponents.

Move $b$ .

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

Multiply $b$ by $b^{2}$ .

Raise $b$ to the power of $1$ .

$- (b^{1} b^{2}) + b^{2} \cdot 3 + 4 b (- b) + 4 b \cdot 3 + 4 (- b) + 4 \cdot 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- b^{1 + 2} + b^{2} \cdot 3 + 4 b (- b) + 4 b \cdot 3 + 4 (- b) + 4 \cdot 3$

Add $1$ and $2$ .

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

Move $3$ to the left of $b^{2}$ .

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

Rewrite using the commutative property of multiplication.

$- b^{3} + 3 b^{2} + 4 \cdot - 1 b \cdot b + 4 b \cdot 3 + 4 (- b) + 4 \cdot 3$

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

Move $b$ .

$- b^{3} + 3 b^{2} + 4 \cdot - 1 (b \cdot b) + 4 b \cdot 3 + 4 (- b) + 4 \cdot 3$

Multiply $b$ by $b$ .

$- b^{3} + 3 b^{2} + 4 \cdot - 1 b^{2} + 4 b \cdot 3 + 4 (- b) + 4 \cdot 3$

Multiply $4$ by $- 1$ .

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

Multiply $3$ by $4$ .

$- b^{3} + 3 b^{2} - 4 b^{2} + 12 b + 4 (- b) + 4 \cdot 3$

Multiply $- 1$ by $4$ .

$- b^{3} + 3 b^{2} - 4 b^{2} + 12 b - 4 b + 4 \cdot 3$

Multiply $4$ by $3$ .

$- b^{3} + 3 b^{2} - 4 b^{2} + 12 b - 4 b + 12$

Simplify by adding terms.

Subtract $4 b^{2}$ from $3 b^{2}$ .

$- b^{3} - b^{2} + 12 b - 4 b + 12$

Subtract $4 b$ from $12 b$ .

$- b^{3} - b^{2} + 8 b + 12$