Pre-Algebra Examples

$16 x^{2} - 81 y^{2}$

Step 1

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

${(4 x)}^{2} - 81 y^{2}$

Step 2

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

${(4 x)}^{2} - {(9 y)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 x$ and $b = 9 y$ .

$(4 x + 9 y) (4 x - (9 y))$

Step 4

Multiply $9$ by $- 1$ .

$(4 x + 9 y) (4 x - 9 y)$