Factor 4x^2-9

$4 x^{2} - 9$

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

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

Rewrite $9$ as $3^{2}$ .

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

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 $b = 3$ .

$(2 x + 3) (2 x - 3)$

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