Precalculus Examples

$x^{2} - 81 y^{2}$

Step 1

Rewrite $81 y^{2}$ as ${(9 y)}^{2}$ .

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

Step 2

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

$(x + 9 y) (x - (9 y))$

Step 3

Multiply $9$ by $- 1$ .

$(x + 9 y) (x - 9 y)$