Precalculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $x$ by $x$ .

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

Step 2.1.2

Combine $x$ and $\frac{1}{4}$ .

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

Step 2.1.3

Combine $x$ and $\frac{1}{4}$ .

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

Step 2.1.4

Multiply $- \frac{1}{4} (- \frac{1}{4})$ .

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Step 2.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.4.2

Multiply $\frac{1}{4}$ by $1$ .

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

Step 2.1.4.3

Multiply $\frac{1}{4}$ by $\frac{1}{4}$ .

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

Step 2.1.4.4

Multiply $4$ by $4$ .

$x^{2} - \frac{x}{4} - \frac{x}{4} + \frac{1}{16}$

Step 2.2

Subtract $\frac{x}{4}$ from $- \frac{x}{4}$ .

$x^{2} - 2 \frac{x}{4} + \frac{1}{16}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $- 2$ .

$x^{2} + 2 (- 1) \frac{x}{4} + \frac{1}{16}$

Step 3.1.2

Factor $2$ out of $4$ .

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

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

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

Step 3.2

Rewrite $- 1 \frac{x}{2}$ as $- \frac{x}{2}$ .

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