Algebra Examples

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

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

Raise $2$ to the power of $4$ .

$\frac{1}{4} \cdot 16 - \frac{1}{2} \cdot {(2)}^{2}$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Factor $4$ out of $16$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 2.3.2

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

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

Step 2.3.3

Cancel the common factor.

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

Step 2.3.4

Rewrite the expression.

$4 - 1 \cdot 2$

Step 2.4

Multiply $- 1$ by $2$ .

$4 - 2$

Step 3

Subtract $2$ from $4$ .

$2$