# How do you factor by grouping 2xz-3z+8x-12y?

Apr 15, 2015

$2 x z - 3 z + 8 x - 12 y$ cannot be factored by grouping.

$\left(2 x z - 3 z\right) + \left(8 x - 12 y\right)$

$= z \left(2 x - 3\right) + 4 \left(2 x - 3 y\right)$ The expressions in parentheses are not the same, so we cannot factor any further.

If we had started with: $2 x z - 3 \textcolor{red}{y} z + 8 x - 12 y$ , the we would get:

$\textcolor{w h i t e}{\text{sssssssssssssssssssss}}$ $\left(2 x z - 3 y z\right) + \left(8 x - 12 y\right)$

$\textcolor{w h i t e}{\text{ssssssssssssssssss}}$ $= z \left(2 x - 3 y\right) + 4 \left(2 x - 3 y\right)$

$\textcolor{w h i t e}{\text{ssssssssssssssssss}}$ $= \left(z + 4\right) \left(2 x - 3 y\right)$