Algebra Examples

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

Step 1

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

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

Step 2

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

${(2 x^{2})}^{2} - {(3 y)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x^{2}$ and $b = 3 y$ .

$(2 x^{2} + 3 y) (2 x^{2} - (3 y))$

Step 4

Multiply $3$ by $- 1$ .

$(2 x^{2} + 3 y) (2 x^{2} - 3 y)$