Algebra Examples

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

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Cancel the common factor of $4$ .

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Step 2.4.1

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

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

Step 2.4.2

Cancel the common factor.

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

Step 2.4.3

Rewrite the expression.

$8 - 1$

Step 3

Subtract $1$ from $8$ .

$7$