Algebra Examples

$n^{4} - 100$

Step 1

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

${(n^{2})}^{2} - 100$

Step 2

Rewrite $100$ as $10^{2}$ .

${(n^{2})}^{2} - 10^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = n^{2}$ and $b = 10$ .

$(n^{2} + 10) (n^{2} - 10)$