Evaluate Using the Given Value 1/2x^4-1/4x^2 for x=2

$\frac{1}{2} x^{4} - \frac{1}{4} x^{2}$ for $x = 2$

Replace the variable $x$ with $2$ in the expression.

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

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of ${(2)}^{4}$ .

$\frac{1}{2} \cdot (2 \cdot 2^{3}) - \frac{1}{4} \cdot {(2)}^{2}$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2^{3}) - \frac{1}{4} \cdot {(2)}^{2}$

Rewrite the expression.

$2^{3} - \frac{1}{4} \cdot {(2)}^{2}$

Raise $2$ to the power of $3$ .

$8 - \frac{1}{4} \cdot {(2)}^{2}$

Raise $2$ to the power of $2$ .

$8 - \frac{1}{4} \cdot 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$8 + \frac{- 1}{4} \cdot 4$

Cancel the common factor.

$8 + \frac{- 1}{4} \cdot 4$

Rewrite the expression.

$8 - 1$

Subtract $1$ from $8$ .

$7$