Find the Product -3v(-8u^2-8uv-7v^2)

$- 3 v (- 8 u^{2} - 8 u v - 7 v^{2})$

Apply the distributive property.

$- 3 v (- 8 u^{2}) - 3 v (- 8 u v) - 3 v (- 7 v^{2})$

Simplify.

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 8 v u^{2} - 3 v (- 8 u v) - 3 v (- 7 v^{2})$

Multiply $v$ by $v$ by adding the exponents.

Move $v$ .

$- 3 \cdot - 8 v u^{2} - 3 (v \cdot v) (- 8 u) - 3 v (- 7 v^{2})$

Multiply $v$ by $v$ .

$- 3 \cdot - 8 v u^{2} - 3 v^{2} (- 8 u) - 3 v (- 7 v^{2})$

Rewrite using the commutative property of multiplication.

$- 3 \cdot - 8 v u^{2} - 3 v^{2} (- 8 u) - 3 \cdot - 7 v \cdot v^{2}$

Simplify each term.

Multiply $- 3$ by $- 8$ .

$24 v u^{2} - 3 v^{2} (- 8 u) - 3 \cdot - 7 v \cdot v^{2}$

Rewrite using the commutative property of multiplication.

$24 v u^{2} - 3 \cdot - 8 v^{2} u - 3 \cdot - 7 v \cdot v^{2}$

Multiply $- 3$ by $- 8$ .

$24 v u^{2} + 24 v^{2} u - 3 \cdot - 7 v \cdot v^{2}$

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

Move $v^{2}$ .

$24 v u^{2} + 24 v^{2} u - 3 \cdot - 7 (v^{2} v)$

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

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

$24 v u^{2} + 24 v^{2} u - 3 \cdot - 7 (v^{2} v^{1})$

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

$24 v u^{2} + 24 v^{2} u - 3 \cdot - 7 v^{2 + 1}$

Add $2$ and $1$ .

$24 v u^{2} + 24 v^{2} u - 3 \cdot - 7 v^{3}$

Multiply $- 3$ by $- 7$ .

$24 v u^{2} + 24 v^{2} u + 21 v^{3}$