Question

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

Answer 1

`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.