limit at h approaches 0 of [(x + h)^2 - x^3] / h

[volleyball_freak31]

Can someone help me find what I am doing wrong? The problem is lim as h approaches 0. [(x+h)^3 - x^3]/h. The answer is 3x^2, heres my work and I keep getting the wrong answer

(x+h) (x+h) = x^2 + 2xh + h^2
(x^2 +2xh +h^2) (x+h) = x^3 + 2x^2h + xh^2 + x^2h+2xh^2 + h^3 - x^3

from there i got it down to x^2 + x, but that is not the right answer

 

[pka]

I cannot follow your algebra.
But it should be:
\(\displaystyle \L
\frac{{\left( {x + h} \right)^3 - x^3 }}{h} = \frac{{x^3 + 3x^2 h + 3xh^2 + h^3 - x^3 }}{h} = \frac{{3x^2 h + 3xh^2 + h^3 }}{h}\)