Factor 25x^2-1

$25 x^{2} - 1$

Step 1

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

${(5 x)}^{2} - 1$

Step 2

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

${(5 x)}^{2} - 1^{2}$

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 $b = 1$ .

$(5 x + 1) (5 x - 1)$