## College Algebra 7th Edition

$3x^{2}+3xh+h^{2}$
We apply the binomial theorem to expand $(x+h)^3$: $(x+h)^3=x^{3}+3x^{2}h^1+3x^1h^{2}+h^{3}$ Now we simplify: $\displaystyle \frac{(x+h)^{3}-x^{3}}{h}=\frac{x^{3}+3x^{2}h+3xh^{2}+h^{3}-x^{3}}{h}=\frac{3x^{2}h+3xh^{2}+h^{3}}{h}=\frac{h(3x^{2}+3xh+h^{2})}{h}=3x^{2}+3xh+h^{2}$