Precalculus Examples

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

Step 1

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

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

Step 2

Expand $(x - \frac{1}{2}) (x - \frac{1}{2})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Combine $x$ and $\frac{1}{2}$ .

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

Step 3.1.3

Combine $x$ and $\frac{1}{2}$ .

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

Step 3.1.4

Multiply $- \frac{1}{2} (- \frac{1}{2})$ .

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.4.2

Multiply $\frac{1}{2}$ by $1$ .

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

Step 3.1.4.3

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

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

Step 3.1.4.4

Multiply $2$ by $2$ .

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

Step 3.2

Subtract $\frac{x}{2}$ from $- \frac{x}{2}$ .

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

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $- 2$ .

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Rewrite $- 1 x$ as $- x$ .

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