Pre-Algebra Examples

$\frac{4 v^{7} - 16 v^{4}}{2 v^{3}}$

Step 1

Factor $4 v^{4}$ out of $4 v^{7} - 16 v^{4}$ .

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Step 1.1

Factor $4 v^{4}$ out of $4 v^{7}$ .

$\frac{4 v^{4} (v^{3}) - 16 v^{4}}{2 v^{3}}$

Step 1.2

Factor $4 v^{4}$ out of $- 16 v^{4}$ .

$\frac{4 v^{4} (v^{3}) + 4 v^{4} (- 4)}{2 v^{3}}$

Step 1.3

Factor $4 v^{4}$ out of $4 v^{4} (v^{3}) + 4 v^{4} (- 4)$ .

$\frac{4 v^{4} (v^{3} - 4)}{2 v^{3}}$

$\frac{4 v^{4} (v^{3} - 4)}{2 v^{3}}$

Step 2

Cancel the common factor of $4$ and $2$ .

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Step 2.1

Factor $2$ out of $4 v^{4} (v^{3} - 4)$ .

$\frac{2 (2 v^{4} (v^{3} - 4))}{2 v^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 v^{3}$ .

$\frac{2 (2 v^{4} (v^{3} - 4))}{2 (v^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (2 v^{4} (v^{3} - 4))}{2 v^{3}}$

Step 2.2.3

Rewrite the expression.

$\frac{2 v^{4} (v^{3} - 4)}{v^{3}}$

$\frac{2 v^{4} (v^{3} - 4)}{v^{3}}$

$\frac{2 v^{4} (v^{3} - 4)}{v^{3}}$

Step 3

Cancel the common factor of $v^{4}$ and $v^{3}$ .

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Step 3.1

Factor $v^{3}$ out of $2 v^{4} (v^{3} - 4)$ .

$\frac{v^{3} (2 v (v^{3} - 4))}{v^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{v^{3} (2 v (v^{3} - 4))}{v^{3} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{v^{3} (2 v (v^{3} - 4))}{v^{3} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{2 v (v^{3} - 4)}{1}$

Step 3.2.4

Divide $2 v (v^{3} - 4)$ by $1$ .

$2 v (v^{3} - 4)$

$2 v (v^{3} - 4)$

$2 v (v^{3} - 4)$

Step 4

Apply the distributive property.

$2 v \cdot v^{3} + 2 v \cdot - 4$

Step 5

Multiply $v$ by $v^{3}$ by adding the exponents.

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Step 5.1

Move $v^{3}$ .

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

Step 5.2

Multiply $v^{3}$ by $v$ .

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Step 5.2.1

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

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

Step 5.2.2

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

$2 v^{3 + 1} + 2 v \cdot - 4$

$2 v^{3 + 1} + 2 v \cdot - 4$

Step 5.3

Add $3$ and $1$ .

$2 v^{4} + 2 v \cdot - 4$

$2 v^{4} + 2 v \cdot - 4$

Step 6

Multiply $- 4$ by $2$ .

$2 v^{4} - 8 v$

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