How do you factor #15ab-12+18a-10b#?

1 Answer
May 24, 2017

Answer:

# (3a-2)(5b+6)#

Explanation:

Let:

# P(x) = 15ab-12+18a-10b#

First we note that there are two terms that contain #a#, so gather these terms up and factor out #a#:

# P(x) = 15ab+18a-12-10b#
# " " = a(15b+18)-12-10b#

The term in brackets also has a common factor of #3#, so:

# P(x) = a(3(5b+6))-12-10b#
# " " = 3a(5b+6)-12-10b#

And for the second terms we have a common factor of #3#,so:

# P(x) = 3a(5b+6)+2(-6-5b)#

We can also factorise #-1# from the second term to get:

# P(x) = 3a(5b+6)-2(6+5b)#
# " " = 3a(5b+6)-2(5b+6)#

Finally, we now have two terms with a common factor of #(5b+6)# so:

# P(x) = (3a-2)(5b+6)#