Basic Math Examples

$(12 u^{3} + 6 u^{2}) \div 2 u$

Step 1

Rewrite the division as a fraction.

$\frac{12 u^{3} + 6 u^{2}}{2 u}$

Step 2

Simplify terms.

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Step 2.1

Factor $6 u^{2}$ out of $12 u^{3} + 6 u^{2}$ .

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Step 2.1.1

Factor $6 u^{2}$ out of $12 u^{3}$ .

$\frac{6 u^{2} (2 u) + 6 u^{2}}{2 u}$

Step 2.1.2

Factor $6 u^{2}$ out of $6 u^{2}$ .

$\frac{6 u^{2} (2 u) + 6 u^{2} (1)}{2 u}$

Step 2.1.3

Factor $6 u^{2}$ out of $6 u^{2} (2 u) + 6 u^{2} (1)$ .

$\frac{6 u^{2} (2 u + 1)}{2 u}$

$\frac{6 u^{2} (2 u + 1)}{2 u}$

Step 2.2

Cancel the common factor of $6$ and $2$ .

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Step 2.2.1

Factor $2$ out of $6 u^{2} (2 u + 1)$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $2$ out of $2 u$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

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

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

Step 2.3

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

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Step 2.3.1

Factor $u$ out of $3 u^{2} (2 u + 1)$ .

$\frac{u (3 u (2 u + 1))}{u}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

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

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

Step 2.3.2.2

Factor $u$ out of $u^{1}$ .

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

Step 2.3.2.3

Cancel the common factor.

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

Step 2.3.2.4

Rewrite the expression.

$\frac{3 u (2 u + 1)}{1}$

Step 2.3.2.5

Divide $3 u (2 u + 1)$ by $1$ .

$3 u (2 u + 1)$

$3 u (2 u + 1)$

$3 u (2 u + 1)$

Step 2.4

Apply the distributive property.

$3 u (2 u) + 3 u \cdot 1$

Step 2.5

Simplify the expression.

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Step 2.5.1

Rewrite using the commutative property of multiplication.

$3 \cdot 2 u \cdot u + 3 u \cdot 1$

Step 2.5.2

Multiply $3$ by $1$ .

$3 \cdot 2 u \cdot u + 3 u$

$3 \cdot 2 u \cdot u + 3 u$

$3 \cdot 2 u \cdot u + 3 u$

Step 3

Simplify each term.

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Step 3.1

Multiply $u$ by $u$ by adding the exponents.

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Step 3.1.1

Move $u$ .

$3 \cdot 2 (u \cdot u) + 3 u$

Step 3.1.2

Multiply $u$ by $u$ .

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

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

Step 3.2

Multiply $3$ by $2$ .

$6 u^{2} + 3 u$

$6 u^{2} + 3 u$

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