Algebra Examples

$25 x^{2} - 49 y^{2}$

Step 1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

${(5 x)}^{2} - 49 y^{2}$

Step 2

Rewrite $49 y^{2}$ as ${(7 y)}^{2}$ .

${(5 x)}^{2} - {(7 y)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x$ and $b = 7 y$ .

$(5 x + 7 y) (5 x - (7 y))$

Step 4

Multiply $7$ by $- 1$ .

$(5 x + 7 y) (5 x - 7 y)$