Answer
$$3{x^2} + 3xh + {h^2}$$
Work Step by Step
$$\eqalign{
& \frac{{{{\left( {x + h} \right)}^3} - {x^3}}}{h},{\text{ for }}h \ne 0 \cr
& {\text{use }}{\left( {a + b} \right)^3} = {a^3} + 3{a^2}b + 3a{b^2} + {b^3}.{\text{ then}} \cr
& = \frac{{{x^3} + 3{x^2}h + 3x{h^2} + {h^3} - {x^3}}}{h} \cr
& {\text{reduce terms}} \cr
& = \frac{{3{x^2}h + 3x{h^2} + {h^3}}}{h} \cr
& {\text{factoring}} \cr
& = \frac{{h\left( {3{x^2} + 3xh + {h^2}} \right)}}{h} \cr
& {\text{cancel h}} \cr
& = 3{x^2} + 3xh + {h^2} \cr} $$
