Evaluate the difference quotient

Evaluate the difference quotient for the given function. Simplify your answer.
F(x)=x^3, (f(a+h)-f(a))/h. I worked it out and received 2a+ha+a^2+2h+h^2. Not sure if it is correct though. Please help, and thanks in advance!

I can tell you that it is incorrect because:
lim (h-->0) (2a + ha + a^2 + 2h + h^2) = 2a + 0 + a^2 + 0 + 0 = 2a + a^2,

which is not the derivative of f(x) at x = a (3a^2).

With f(x) = x^3, we see that:
f(a + h) = (a + h)^3 and f(a) = a^3.

Then, we see that:
[f(a + h) - f(a)]/h = [(a + h)^3 - a^3]/h
= (a^3 + 3a^2*h + 3ah^2 + h^3 - a^3)/h, by binomial expansion
= (3a^2*h + 3ah^2 + h^3)/h
= [h(3a^2 + 3ah + h^2)]/h, by factoring the numerator
= 3a^2 + 3ah + h^2, by canceling h.

I hope this helps!