Pre-Algebra Examples

$4 x^{2} - 25 y^{2}$

Step 1

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

${(2 x)}^{2} - 25 y^{2}$

Step 2

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

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

Step 3

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

$(2 x + 5 y) (2 x - (5 y))$

Step 4

Multiply $5$ by $- 1$ .

$(2 x + 5 y) (2 x - 5 y)$