How do you factor #15a^2b^2-20ab^2+10ab^3#?

1 Answer
Nov 16, 2015

Answer:

#15a^2b^2-20ab^2+10ab^3=5ab^2(3a - 4 + 2b)#

Explanation:

Looking at each of the terms, we can see that #15#, #20#, and #10# have the greatest common divisor of #5#. Additionally, the highest shared power of #a# between terms is #a^1# and the highest shared power of #b# is #b^2#.
Thus we know that they all have a common factor of #5ab^2#. Factoring this out gives us

#15a^2b^2-20ab^2+10ab^3=5ab^2(3a - 4 + 2b)#

As there are no more shared divisors between terms, nor powers greater than one, we can be satisfied that this is the complete factorization.