Hi Ema.

The technical name for that kind of algebraic expression is a bivariate polynomial.

I'm going to do a similar problem to yours to show you the technique.

Factor completely:
4a⁷b³ - 10a⁶b² - 24a⁵b.

Solution:
All the terms are even, so I can factor out a 2.
All the terms have at least a⁵ in them.
All the terms have at least b in them.
So factor out a 2a⁵b first.

2a⁵b (2a²b² - 5ab - 12)

Now I can see that what is in the parentheses is in the form of Ax² + Bx + C, where in this case x = ab and A, B, and C are all constants. So this is actually a normal trinomial like you've solved before. In this case, you have 2x² - 5x - 12. Use normal decomposition factoring to break this down. If you aren't sure about that, Penny wrote a good description here. You get (2x + 3)(x - 4). Then we can replace x with ab.

Since 2a²b² - 5ab - 12 = (2ab + 3)(ab - 4), my final answer is 2a⁵b(2ab + 3)(ab - 4).

Hope this helps,
Stephen La Rocque.