First, you're going to find the LCM (Least Common Multiple):
#5ab^2#
Next, you're actually going to factor everything out! So...
#15a^2b^3 + 10a^2b^2 - 5ab^3# =
#5ab^2(3ab + 2a - 1b)#
There's your answer!
The way you factor this out is by dividing the outside of the parentheses (#5ab^2#) by the inside of the parentheses (#3ab + 2ab - 1b#). Our first division is #(5ab^2)/(15a^2b^3)#. We are first going to divide #15/5#, which equals #3#. Next, we are going to divide all of the numbers. Let's start with #'a'#. #(a^2)/(a)# is going to equal #a^1#, or just #a#. So far, we have #3a#. Let's continue with #'b'#. #(b^3)/(b^2)# is going to equal #b^1#, or just #b#. So your first factored number is #3ab# !
Just continue these steps and you will get every single factoring there ever is!
