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

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Answer 1 · 2015-04-29T11:12:27

#−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

# = -15ac(b + c) + 3c(b+c)#

#(b+c)# is a common factor to each of the terms now

# = (b+c)(-15ac + 3c)#

# = (b+c)(3c - 15ac )#

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

# = (b+c){3c(1 - 5a)}#

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