# How do you simplify 9x^2-5x^4?

Sep 28, 2015

$9 {x}^{2} - 5 {x}^{4} = {x}^{2} \left(3 - \sqrt{5} x\right) \left(3 + \sqrt{5} x\right)$

#### Explanation:

$9 {x}^{2} - 5 {x}^{2}$

$\textcolor{w h i t e}{\text{XXX}}$extracting the obvious factor of ${x}^{2}$
$= {x}^{2} \left(9 - 5 {x}^{2}\right)$

$\textcolor{w h i t e}{\text{XXX}}$remember that $\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$
$\textcolor{w h i t e}{\text{XXX}}$and substituting $9 = {3}^{2}$ for ${a}^{2}$
$\textcolor{w h i t e}{\text{XXX}}$and $5 {x}^{2} = {\left(\sqrt{5} x\right)}^{2}$ for ${b}^{2}$
$= {x}^{2} \left(3 - \sqrt{5} x\right) \left(3 + \sqrt{5} x\right)$