Simplify (1-x/2)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

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

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

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

Multiply $- 1$ by $1$ .

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Multiply $2$ by $2$ .

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

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

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

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify (1-x/2)^2

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