Factorize $15a^2b^3 - 5a^3b^2 - 10a^4b$

Question

I'm having problems with the factorization of $15a^2b^3 - 5a^3b^2 - 10a^4b$. I get stuck on step 2.

1: $15a^2b^3 - 5a^3b^2 - 10a^4b$

2: $5a^2b (3b^2 - ab - 2a^2)$

How do I factorize $3b^2 - ab - 2a^2$?

Thank you!

Answer 1

Use the 'AC' method , $$3 \cdot (-2) = -6$$

next find two numbers that multipply to $-6$ and sum to $-1$ , those two numbers are $-3$ , $2$. Now regroup like so ,

$$(3b^2 - 3ab) + (2ab - 2a^2)$$

Can you finish it now?