Precalculus Examples

$\frac{1}{4} x^{2} - 16$

Step 1

Rewrite $\frac{1}{4} x^{2}$ as ${(\frac{1}{2} x)}^{2}$ .

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

Step 2

Rewrite $16$ as $4^{2}$ .

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{1}{2} x$ and $b = 4$ .

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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