Algebra Examples

$a^{4} - 9$

Step 1

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

${(a^{2})}^{2} - 9$

Step 2

Rewrite $9$ as $3^{2}$ .

${(a^{2})}^{2} - 3^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a^{2}$ and $b = 3$ .

$(a^{2} + 3) (a^{2} - 3)$