How do you factor by grouping #15b^2-22bc-5c^2#?

Question

1425 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-03T07:05:19

To solve this using Grouping, we need 4 terms.

We can split the middle term of this expression to get 4 terms

We need to think of 2 numbers such that:

#N_1*N_2 = 15*-5 = -75#
AND
#N_1 +N_2 = -22#

After trying out a few numbers we get #N_1 = -25# and #N_2 =3#

#-25*3 = -75#, and #-25+3= -22#

We write the expression as:

#15b^2-25bc+3bc-5c^2#

We make Groups of two terms:

#=(15b^2-25bc)+(3bc-5c^2)#

# = 5b(3b - 5c) + c(3b - 5c)#

#3b-5c# is a Common Factor to each of the terms

# = color(green)((3b-5c)(5b+c)#