What is the factors for 4x^2 -9?

May 6, 2015

$4 {x}^{2} - 9 = {\left(2 x\right)}^{2} - {3}^{2}$

We know that color(blue)(a^2 - b^2 = (a+b)(a-b)

Hence ${\left(2 x\right)}^{2} - {3}^{2} = \left(2 x + 3\right) \left(2 x - 3\right)$

The factors of $4 {x}^{2} - 9$ are color(green)((2x + 3) and color(green)((2x - 3)

May 6, 2015

The answer is $\left(4 {x}^{2} - 9\right) = \left(2 x - 3\right) \left(2 x + 3\right)$.

This is an example of the difference of squares, where $\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$.

$\left(4 {x}^{2} - 9\right) = \left({\left(2 x\right)}^{2} - {3}^{2}\right)$

$a = 2 x$
$b = 3$

$\left(4 {x}^{2} - 9\right) = \left(2 x - 3\right) \left(2 x + 3\right)$