a^2b(3a^2 + 4ab^2)

a²b(3a² + 4ab²) = 3a⁴b + 4a³b³

distribute so u get 3a^4b+(4a^2*b)^4b

hihihihihihihihi

You haven't actually asked a question but Alan has expanded and simplified your expression.

Our anonymous guest made a little error.  But I like to see people 'having a go' so thankyou.