Algebra Examples

$- 2 (4 v^{2} + 5 v) + v (v^{2} + 6 v)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 2 (4 v^{2}) - 2 (5 v) + v (v^{2} + 6 v)$

Step 1.2

Multiply $4$ by $- 2$ .

$- 8 v^{2} - 2 (5 v) + v (v^{2} + 6 v)$

Step 1.3

Multiply $5$ by $- 2$ .

$- 8 v^{2} - 10 v + v (v^{2} + 6 v)$

Step 1.4

Apply the distributive property.

$- 8 v^{2} - 10 v + v \cdot v^{2} + v (6 v)$

Step 1.5

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

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Step 1.5.1

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

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Step 1.5.1.1

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

$- 8 v^{2} - 10 v + v^{1} v^{2} + v (6 v)$

Step 1.5.1.2

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

$- 8 v^{2} - 10 v + v^{1 + 2} + v (6 v)$

$- 8 v^{2} - 10 v + v^{1 + 2} + v (6 v)$

Step 1.5.2

Add $1$ and $2$ .

$- 8 v^{2} - 10 v + v^{3} + v (6 v)$

$- 8 v^{2} - 10 v + v^{3} + v (6 v)$

Step 1.6

Rewrite using the commutative property of multiplication.

$- 8 v^{2} - 10 v + v^{3} + 6 v \cdot v$

Step 1.7

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

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Step 1.7.1

Move $v$ .

$- 8 v^{2} - 10 v + v^{3} + 6 (v \cdot v)$

Step 1.7.2

Multiply $v$ by $v$ .

$- 8 v^{2} - 10 v + v^{3} + 6 v^{2}$

$- 8 v^{2} - 10 v + v^{3} + 6 v^{2}$

$- 8 v^{2} - 10 v + v^{3} + 6 v^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 8 v^{2}$ and $6 v^{2}$ .

$- 2 v^{2} - 10 v + v^{3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Move $- 10 v$ .

$- 2 v^{2} + v^{3} - 10 v$

Step 2.2.2

Reorder $- 2 v^{2}$ and $v^{3}$ .

$v^{3} - 2 v^{2} - 10 v$

$v^{3} - 2 v^{2} - 10 v$

$v^{3} - 2 v^{2} - 10 v$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$