# How do you factor by grouping 224az+56ac-84yz-21yc?

May 17, 2015

First notice that all the coefficients are divisible by 7, so let's separate out that factor first...

$224 a z + 56 a c - 84 y z - 21 y c$

$= 7 \left(32 a z + 8 a c - 12 y z - 3 y c\right)$

$= 7 \left(\left(32 a z + 8 a c\right) - \left(12 y z + 3 y c\right)\right)$

$= 7 \left(8 a \left(4 z + c\right) - 3 y \left(4 z + c\right)\right)$

$= 7 \left(8 a - 3 y\right) \left(4 z + c\right)$