# How do you factor g^4-1?

Mar 30, 2018

$\left(g + 1\right) \left(g - 1\right) \left({g}^{2} + 1\right)$

#### Explanation:

We are looking at the sum of two squares

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

So applying that rule we get
$\left({g}^{2} - 1\right) \left({g}^{2} + 1\right)$

We can also see that the $\left({g}^{2} - 1\right)$ term is also a sum of two squares so it now looks like

$\left(g + 1\right) \left(g - 1\right) \left({g}^{2} + 1\right)$