# How do you factor by grouping −15abc − 15ac^2 + 3bc + 3c^2?

Apr 29, 2015

−15abc − 15ac^2 + 3bc + 3c^2

We can factor this expression by making groups of 2 terms

= (−15abc − 15ac^2) + (3bc + 3c^2)

Now we take the common factors out from each group

$= - 15 a c \left(b + c\right) + 3 c \left(b + c\right)$

$\left(b + c\right)$ is a common factor to each of the terms now

$= \left(b + c\right) \left(- 15 a c + 3 c\right)$

$= \left(b + c\right) \left(3 c - 15 a c\right)$

The factor $3 c$ is common to the terms in the second group above

$= \left(b + c\right) \left\{3 c \left(1 - 5 a\right)\right\}$

 =color(green)( 3c(b+c)(1-5a) is the Factorised form of −15abc − 15ac^2 + 3bc + 3c^2