# How do you factor 4a^4 + b^4?

Jun 6, 2016

$4 {a}^{4} + {b}^{4} = \left(2 {a}^{2} + {b}^{2} i\right) \left(2 {a}^{2} - {b}^{2} i\right)$

#### Explanation:

Given,

$4 {a}^{4} + {b}^{4}$

Rewrite each term such that both terms have an exponent of $2$.

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

Recall that the expression follows the sum of squares pattern, $\textcolor{red}{{x}^{2}} + \textcolor{b l u e}{{y}^{2}} = \left(\textcolor{red}{x} \textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{+} \textcolor{b l u e}{y} \textcolor{p u r p \le}{i}\right) \left(\textcolor{red}{x} \textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{-} \textcolor{b l u e}{y} \textcolor{p u r p \le}{i}\right)$. Thus,

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\left(2 {a}^{2} + {b}^{2} i\right) \left(2 {a}^{2} - {b}^{2} i\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$