Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

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

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Step 2.2.1

Move $v$ .

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

Step 2.2.2

Multiply $v$ by $v$ .

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

Step 2.3

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $- 3$ by $- 8$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

Multiply $- 3$ by $- 8$ .

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

Step 3.4

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

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Step 3.4.1

Move $v^{2}$ .

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

Step 3.4.2

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

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Step 3.4.2.1

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

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

Step 3.4.2.2

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

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

Step 3.4.3

Add $2$ and $1$ .

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

Step 3.5

Multiply $- 3$ by $- 7$ .

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