Algebra Examples

$81 x^{2} - 121 y^{2}$

Step 1

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

${(9 x)}^{2} - 121 y^{2}$

Step 2

Rewrite $121 y^{2}$ as ${(11 y)}^{2}$ .

${(9 x)}^{2} - {(11 y)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 9 x$ and $b = 11 y$ .

$(9 x + 11 y) (9 x - (11 y))$

Step 4

Multiply $11$ by $- 1$ .

$(9 x + 11 y) (9 x - 11 y)$