Trigonometry Examples

$(\frac{x}{4} + \frac{1}{3}) \cdot (\frac{x}{4} - \frac{1}{3})$

Step 1

Expand $(\frac{x}{4} + \frac{1}{3}) (\frac{x}{4} - \frac{1}{3})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\frac{x}{4} (\frac{x}{4} - \frac{1}{3}) + \frac{1}{3} (\frac{x}{4} - \frac{1}{3})$

Step 1.2

Apply the distributive property.

$\frac{x}{4} \cdot \frac{x}{4} + \frac{x}{4} (- \frac{1}{3}) + \frac{1}{3} (\frac{x}{4} - \frac{1}{3})$

Step 1.3

Apply the distributive property.

$\frac{x}{4} \cdot \frac{x}{4} + \frac{x}{4} (- \frac{1}{3}) + \frac{1}{3} \cdot \frac{x}{4} + \frac{1}{3} (- \frac{1}{3})$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $\frac{x}{4} \cdot \frac{x}{4} + \frac{x}{4} (- \frac{1}{3}) + \frac{1}{3} \cdot \frac{x}{4} + \frac{1}{3} (- \frac{1}{3})$ .

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Step 2.1.1

Reorder the factors in the terms $\frac{x}{4} (- \frac{1}{3})$ and $\frac{1}{3} \cdot \frac{x}{4}$ .

$\frac{x}{4} \cdot \frac{x}{4} - \frac{1}{3} \cdot \frac{x}{4} + \frac{1}{3} \cdot \frac{x}{4} + \frac{1}{3} (- \frac{1}{3})$

Step 2.1.2

Add $- \frac{1}{3} \cdot \frac{x}{4}$ and $\frac{1}{3} \cdot \frac{x}{4}$ .

$\frac{x}{4} \cdot \frac{x}{4} + 0 + \frac{1}{3} (- \frac{1}{3})$

Step 2.1.3

Add $\frac{x}{4} \cdot \frac{x}{4}$ and $0$ .

$\frac{x}{4} \cdot \frac{x}{4} + \frac{1}{3} (- \frac{1}{3})$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $\frac{x}{4} \cdot \frac{x}{4}$ .

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Step 2.2.1.1

Multiply $\frac{x}{4}$ by $\frac{x}{4}$ .

$\frac{x \cdot x}{4 \cdot 4} + \frac{1}{3} (- \frac{1}{3})$

Step 2.2.1.2

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

$\frac{x^{1} x}{4 \cdot 4} + \frac{1}{3} (- \frac{1}{3})$

Step 2.2.1.3

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

$\frac{x^{1} x^{1}}{4 \cdot 4} + \frac{1}{3} (- \frac{1}{3})$

Step 2.2.1.4

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

$\frac{x^{1 + 1}}{4 \cdot 4} + \frac{1}{3} (- \frac{1}{3})$

Step 2.2.1.5

Add $1$ and $1$ .

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

Step 2.2.1.6

Multiply $4$ by $4$ .

$\frac{x^{2}}{16} + \frac{1}{3} (- \frac{1}{3})$

Step 2.2.2

Multiply $\frac{1}{3} (- \frac{1}{3})$ .

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Step 2.2.2.1

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

$\frac{x^{2}}{16} - \frac{1}{3 \cdot 3}$

Step 2.2.2.2

Multiply $3$ by $3$ .

$\frac{x^{2}}{16} - \frac{1}{9}$