Basic Math Examples

$(\frac{a}{b} + 3) (\frac{a}{b} + 3)$

Step 1

Expand $(\frac{a}{b} + 3) (\frac{a}{b} + 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\frac{a}{b} (\frac{a}{b} + 3) + 3 (\frac{a}{b} + 3)$

Step 1.2

Apply the distributive property.

$\frac{a}{b} \cdot \frac{a}{b} + \frac{a}{b} \cdot 3 + 3 (\frac{a}{b} + 3)$

Step 1.3

Apply the distributive property.

$\frac{a}{b} \cdot \frac{a}{b} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $\frac{a}{b} \cdot \frac{a}{b}$ .

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Step 2.1.1.1

Multiply $\frac{a}{b}$ by $\frac{a}{b}$ .

$\frac{a \cdot a}{b \cdot b} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.2

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

$\frac{a^{1} a}{b \cdot b} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.3

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

$\frac{a^{1} a^{1}}{b \cdot b} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.4

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

$\frac{a^{1 + 1}}{b \cdot b} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.5

Add $1$ and $1$ .

$\frac{a^{2}}{b \cdot b} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.6

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

$\frac{a^{2}}{b^{1} b} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.7

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

$\frac{a^{2}}{b^{1} b^{1}} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.8

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

$\frac{a^{2}}{b^{1 + 1}} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.1.9

Add $1$ and $1$ .

$\frac{a^{2}}{b^{2}} + \frac{a}{b} \cdot 3 + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.2

Combine $\frac{a}{b}$ and $3$ .

$\frac{a^{2}}{b^{2}} + \frac{a \cdot 3}{b} + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.3

Move $3$ to the left of $a$ .

$\frac{a^{2}}{b^{2}} + \frac{3 \cdot a}{b} + 3 \frac{a}{b} + 3 \cdot 3$

Step 2.1.4

Combine $3$ and $\frac{a}{b}$ .

$\frac{a^{2}}{b^{2}} + \frac{3 a}{b} + \frac{3 a}{b} + 3 \cdot 3$

Step 2.1.5

Multiply $3$ by $3$ .

$\frac{a^{2}}{b^{2}} + \frac{3 a}{b} + \frac{3 a}{b} + 9$

Step 2.2

Add $\frac{3 a}{b}$ and $\frac{3 a}{b}$ .

$\frac{a^{2}}{b^{2}} + 2 \frac{3 a}{b} + 9$

Step 3

Multiply $2 \frac{3 a}{b}$ .

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Step 3.1

Combine $2$ and $\frac{3 a}{b}$ .

$\frac{a^{2}}{b^{2}} + \frac{2 (3 a)}{b} + 9$

Step 3.2

Multiply $3$ by $2$ .

$\frac{a^{2}}{b^{2}} + \frac{6 a}{b} + 9$