Basic Math Examples

$\frac{18 a^{3} + 30 a^{2}}{3 a}$

Step 1

Simplify terms.

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Step 1.1

Factor $6 a^{2}$ out of $18 a^{3} + 30 a^{2}$ .

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Step 1.1.1

Factor $6 a^{2}$ out of $18 a^{3}$ .

$\frac{6 a^{2} (3 a) + 30 a^{2}}{3 a}$

Step 1.1.2

Factor $6 a^{2}$ out of $30 a^{2}$ .

$\frac{6 a^{2} (3 a) + 6 a^{2} (5)}{3 a}$

Step 1.1.3

Factor $6 a^{2}$ out of $6 a^{2} (3 a) + 6 a^{2} (5)$ .

$\frac{6 a^{2} (3 a + 5)}{3 a}$

$\frac{6 a^{2} (3 a + 5)}{3 a}$

Step 1.2

Cancel the common factor of $6$ and $3$ .

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Step 1.2.1

Factor $3$ out of $6 a^{2} (3 a + 5)$ .

$\frac{3 (2 a^{2} (3 a + 5))}{3 a}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $3$ out of $3 a$ .

$\frac{3 (2 a^{2} (3 a + 5))}{3 (a)}$

Step 1.2.2.2

Cancel the common factor.

$\frac{3 (2 a^{2} (3 a + 5))}{3 a}$

Step 1.2.2.3

Rewrite the expression.

$\frac{2 a^{2} (3 a + 5)}{a}$

$\frac{2 a^{2} (3 a + 5)}{a}$

$\frac{2 a^{2} (3 a + 5)}{a}$

Step 1.3

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

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Step 1.3.1

Factor $a$ out of $2 a^{2} (3 a + 5)$ .

$\frac{a (2 a (3 a + 5))}{a}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

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

$\frac{a (2 a (3 a + 5))}{a^{1}}$

Step 1.3.2.2

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

$\frac{a (2 a (3 a + 5))}{a \cdot 1}$

Step 1.3.2.3

Cancel the common factor.

$\frac{a (2 a (3 a + 5))}{a \cdot 1}$

Step 1.3.2.4

Rewrite the expression.

$\frac{2 a (3 a + 5)}{1}$

Step 1.3.2.5

Divide $2 a (3 a + 5)$ by $1$ .

$2 a (3 a + 5)$

$2 a (3 a + 5)$

$2 a (3 a + 5)$

Step 1.4

Apply the distributive property.

$2 a (3 a) + 2 a \cdot 5$

Step 1.5

Simplify the expression.

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Step 1.5.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 a \cdot a + 2 a \cdot 5$

Step 1.5.2

Multiply $5$ by $2$ .

$2 \cdot 3 a \cdot a + 10 a$

$2 \cdot 3 a \cdot a + 10 a$

$2 \cdot 3 a \cdot a + 10 a$

Step 2

Simplify each term.

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Step 2.1

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1.1

Move $a$ .

$2 \cdot 3 (a \cdot a) + 10 a$

Step 2.1.2

Multiply $a$ by $a$ .

$2 \cdot 3 a^{2} + 10 a$

$2 \cdot 3 a^{2} + 10 a$

Step 2.2

Multiply $2$ by $3$ .

$6 a^{2} + 10 a$

$6 a^{2} + 10 a$

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