Simplify (x^2-1/2)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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

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

Add $2$ and $2$ .

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

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

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

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

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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