Algebra Examples

$x^{2 n} - 81$

Step 1

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

${(x^{n})}^{2} - 81$

Step 2

Rewrite $81$ as $9^{2}$ .

${(x^{n})}^{2} - 9^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{n}$ and $b = 9$ .

$(x^{n} + 9) (x^{n} - 9)$