# How do you factor the expression 9x^2-25?

Jan 6, 2016

${\left(3 x\right)}^{2} - {\left(5\right)}^{2} = \left(3 x + 5\right) \left(3 x - 5\right)$
$9 {x}^{2} - 25$ fits the form ${a}^{2} - {b}^{2}$, where $a = 3 x$ and $b = 5$. Rewrite the expression as ${\left(3 x\right)}^{2} - {\left(5\right)}^{2}$.
Use the difference of squares: ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$.
${\left(3 x\right)}^{2} - {\left(5\right)}^{2} = \left(3 x + 5\right) \left(3 x - 5\right)$