Algebra Examples

$\frac{4 x^{2} - 1}{x^{2}}$

Step 1

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

$\frac{{(2 x)}^{2} - 1}{x^{2}}$

Step 2

Rewrite $1$ as $1^{2}$ .

$\frac{{(2 x)}^{2} - 1^{2}}{x^{2}}$

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 $b = 1$ .

$\frac{(2 x + 1) (2 x - 1)}{x^{2}}$