Q: Prove that the set of rational numbers form a group under the operation * where a * b = 2a + 3b + 4ab

I have to prove (a * b) * c = a * (b * c)

After some working and simplifying, I get

(a * b) * c = 12a + 18b + 24ab + 4c

This is the first half of the proof (for associativity)

The second part, a * y = 2a + 6b + 9c + 12bc + 8ab + 12ac + 16abc

I don't think this can be simplified to equal my first result, but it has to; please help me