Find the Product -4b(1-9b-2b^2)

$- 4 b (1 - 9 b - 2 b^{2})$

Apply the distributive property.

$- 4 b \cdot 1 - 4 b (- 9 b) - 4 b (- 2 b^{2})$

Simplify.

Multiply $- 4$ by $1$ .

$- 4 b - 4 b (- 9 b) - 4 b (- 2 b^{2})$

Rewrite using the commutative property of multiplication.

$- 4 b - 4 \cdot - 9 b \cdot b - 4 b (- 2 b^{2})$

Rewrite using the commutative property of multiplication.

$- 4 b - 4 \cdot - 9 b \cdot b - 4 \cdot - 2 b \cdot b^{2}$

Simplify each term.

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

Move $b$ .

$- 4 b - 4 \cdot - 9 (b \cdot b) - 4 \cdot - 2 b \cdot b^{2}$

Multiply $b$ by $b$ .

$- 4 b - 4 \cdot - 9 b^{2} - 4 \cdot - 2 b \cdot b^{2}$

Multiply $- 4$ by $- 9$ .

$- 4 b + 36 b^{2} - 4 \cdot - 2 b \cdot b^{2}$

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

Move $b^{2}$ .

$- 4 b + 36 b^{2} - 4 \cdot - 2 (b^{2} b)$

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

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

$- 4 b + 36 b^{2} - 4 \cdot - 2 (b^{2} b^{1})$

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

$- 4 b + 36 b^{2} - 4 \cdot - 2 b^{2 + 1}$

Add $2$ and $1$ .

$- 4 b + 36 b^{2} - 4 \cdot - 2 b^{3}$

Multiply $- 4$ by $- 2$ .

$- 4 b + 36 b^{2} + 8 b^{3}$