# How do you factor f(x)= x^4 - 9x^2?

May 15, 2018

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

#### Explanation:

${x}^{4} - 9 {x}^{2}$

take ${x}^{2}$ as a common factor:

$\textcolor{red}{{x}^{2}} \cdot \left({x}^{2} - 9\right)$

now what is inside the parentheses we can factor them by the difference between two squares formula: $\textcolor{b l u e}{{x}^{2} - 9 = {x}^{2} - {3}^{2}}$

now difference between two squares formula

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

$\textcolor{b l u e}{{x}^{2} - {3}^{2} = \left(x - 3\right) \left(x + 3\right)}$

$= \textcolor{red}{{x}^{2}} \cdot \textcolor{b l u e}{\left(x - 3\right) \left(x + 3\right)}$

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