Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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