Basic Math Examples

$\frac{9 u^{5} - 18 u^{4}}{3 u^{2}}$

Step 1

Factor $9 u^{4}$ out of $9 u^{5} - 18 u^{4}$ .

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Step 1.1

Factor $9 u^{4}$ out of $9 u^{5}$ .

$\frac{9 u^{4} (u) - 18 u^{4}}{3 u^{2}}$

Step 1.2

Factor $9 u^{4}$ out of $- 18 u^{4}$ .

$\frac{9 u^{4} (u) + 9 u^{4} (- 2)}{3 u^{2}}$

Step 1.3

Factor $9 u^{4}$ out of $9 u^{4} (u) + 9 u^{4} (- 2)$ .

$\frac{9 u^{4} (u - 2)}{3 u^{2}}$

$\frac{9 u^{4} (u - 2)}{3 u^{2}}$

Step 2

Cancel the common factor of $9$ and $3$ .

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Step 2.1

Factor $3$ out of $9 u^{4} (u - 2)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

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

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

Step 3

Cancel the common factor of $u^{4}$ and $u^{2}$ .

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Step 3.1

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

$\frac{u^{2} (3 u^{2} (u - 2))}{u^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

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

$3 u^{2} (u - 2)$

$3 u^{2} (u - 2)$

$3 u^{2} (u - 2)$

Step 4

Apply the distributive property.

$3 u^{2} u + 3 u^{2} \cdot - 2$

Step 5

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

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Step 5.1

Move $u$ .

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

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

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

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

Step 5.3

Add $1$ and $2$ .

$3 u^{3} + 3 u^{2} \cdot - 2$

$3 u^{3} + 3 u^{2} \cdot - 2$

Step 6

Multiply $- 2$ by $3$ .

$3 u^{3} - 6 u^{2}$

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