# How do you factor by grouping 2m^4 + 6 - am^4 - 3a?

Jul 23, 2015

Extract factors from $2 {m}^{4} + 6$ and $- a {m}^{4} - 3 a$ leaving a factor common to both; then extract that factor:
$\textcolor{w h i t e}{\text{XXXX}}$$2 {m}^{4} + 6 - a {m}^{4} - 3 a = \left(2 - a\right) \left({m}^{4} + 3\right)$

#### Explanation:

$2 {m}^{4} + 6 - a {m}^{4} - 3 a$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left(\textcolor{red}{2 {m}^{4} + 6}\right) - \left(\textcolor{b l u e}{a {m}^{4} + 3 a}\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \textcolor{red}{2} \left({m}^{4} + 3\right) - \textcolor{b l u e}{a} \left({m}^{4} + 3\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \left(2 - a\right) \left({m}^{4} + 3\right)$