Factor (4x^2-1)

$(4 x^{2} - 1)$

Remove parentheses.

$4 x^{2} - 1$

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

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

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

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

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 $b = 1$ .

$(2 x + 1) (2 x - 1)$