Algebra Examples

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

Step 1

Combine fractions.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $2$ by $2$ .

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

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

$4 - x - \frac{x}{2} \cdot 2 - \frac{x}{2} (- \frac{x}{2})$

Step 3.1.3

Cancel the common factor of $2$ .

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Step 3.1.3.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

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

Step 3.1.3.2

Cancel the common factor.

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

Step 3.1.3.3

Rewrite the expression.

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

Step 3.1.4

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

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Step 3.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.4.2

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

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

Step 3.1.4.3

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

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

Step 3.1.4.4

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

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

Step 3.1.4.5

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

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

Step 3.1.4.6

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

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

Step 3.1.4.7

Add $1$ and $1$ .

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

Step 3.1.4.8

Multiply $2$ by $2$ .

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

Step 3.2

Subtract $x$ from $- x$ .

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