First, you're going to find the LCM (Least Common Multiple):
5ab^25ab2
Next, you're actually going to factor everything out! So...
15a^2b^3 + 10a^2b^2 - 5ab^315a2b3+10a2b2−5ab3 =
5ab^2(3ab + 2a - 1b)5ab2(3ab+2a−1b)
There's your answer!
The way you factor this out is by dividing the outside of the parentheses (5ab^25ab2) by the inside of the parentheses (3ab + 2ab - 1b3ab+2ab−1b). Our first division is (5ab^2)/(15a^2b^3)5ab215a2b3. We are first going to divide 15/5155, which equals 33. 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!