# How do you factor completely a^4-b^4 ?

Apr 19, 2016

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

#### Explanation:

In algebra, there is a formula known as the Difference of two squares: $\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \left(a - b\right)$

In the case of ${a}^{4} - {b}^{4}$, you'll see that ${a}^{4}$ is just ${\left({a}^{2}\right)}^{2}$ and ${b}^{4}$ is just ${\left({b}^{2}\right)}^{2}$:
${a}^{4} - {b}^{4} = {\left({a}^{2}\right)}^{2} - {\left({b}^{2}\right)}^{2}$
$= \left({a}^{2} + {b}^{2}\right) \left({a}^{2} - {b}^{2}\right)$
But as you can see, we can use the formula again:
$= \left({a}^{2} + {b}^{2}\right) \left(a + b\right) \left(a - b\right)$
And this is the final answer