Precalculus Examples

$u^{2} v^{2} - 225$

Step 1

Rewrite $u^{2} v^{2}$ as ${(u v)}^{2}$ .

${(u v)}^{2} - 225$

Step 2

Rewrite $225$ as $15^{2}$ .

${(u v)}^{2} - 15^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = u v$ and $b = 15$ .

$(u v + 15) (u v - 15)$