Algebra Examples

$x^{4} - 25$

Step 1

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

${(x^{2})}^{2} - 25$

Step 2

Rewrite $25$ as $5^{2}$ .

${(x^{2})}^{2} - 5^{2}$

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 $b = 5$ .

$(x^{2} + 5) (x^{2} - 5)$