(f(a+h) - f(a))/h = ((a^3+3a^2h + 3ah^2 + h^3) - a^3)/h
Using the distributive property and combining like terms in the numerator, we have:
(f(a+h) - f(a))/h = ((a^3 + 3a^2h + 3ah^2 + h^3) - a^3)/h
= (3a^2h + 3ah^2 + h^3)/h
Now, we can cancel out the h in the numerator and denominator:
(f(a+h) - f(a))/h = 3a^2 + 3ah + h^2
Therefore, the final answer is (f(a+h) - f(a))/h = 3a^2 + 3ah + h^2.