You are on the right track with expanding all 3 equations.

Do the same for all three equations:

(1) 254 = ab^2 + cb + d

(2) 330 = a(b+1)^2 + c(b+1) + d

(3) 416 = a(b+2)^2 + c(b+2) + d

Note that d is a common term in all the equations - can you find a way to get rid of it, so you have 3 equations with 3 unknowns?