How do you factor by grouping 12xy- 8x + 42y - 28?

May 17, 2015

$12 x y - 8 x + 42 y - 28$

We factor this expression by making groups of 2 terms
$= \left(12 x y - 8 x\right) + \left(42 y - 28\right)$

Now we take the common factors out from each group
$= 4 x \left(3 y - 2\right) + 14 \left(3 y - 2\right)$

$\left(3 y - 2\right)$ is a common factor to each of the terms now:
$= \left(3 y - 2\right) \left(4 x + 14\right)$

$2$ is common to the terms in the second group above
$= \left(3 y - 2\right) \left\{2 \left(2 x + 7\right)\right\}$

 color(green)( (3y -2){2(2x+ 7)} is the Factorised form of $12 x y - 8 x + 42 y - 28$