Question 152517
I think I understand what you mean.
{{{g(x)=x^3}}}
Let x=2+h,
{{{g(2+h)=(2+h)^3}}}
{{{g(2+h)=(2+h)*(2+h)*(2+h)}}}
Let's break it down a little and work on {{{(2+h)*(2+h)}}} first.
Use the FOIL (First, Outer, Inner, Last) method,
First : {{{(highlight(2)+h)(highlight(2)+h)=(2)(2)=4}}}
Outer : {{{(highlight(2)+h)(2+highlight(h))=(2)(h)=2h}}}
Inner : {{{(2+highlight(h))(highlight(2)+h)=(h)(2)=2h}}}
Outer : {{{(2+highlight(h))(2+highlight(h))=(h)(h)=h^2}}}
Add them all together,
{{{(2+h)*(2+h)=4+2h+2h+h^2}}}
{{{(2+h)*(2+h)=4+4h+h^2}}}
Now substitute that back in,
{{{g(2+h)=(2+h)*(2+h)*(2+h)}}}
{{{g(2+h)=(4+4h+h^2)*(2+h)}}}
Distribute the {{{(2+h)}}} term,
{{{g(2+h)=4(2+h)+4h(2+h)+h^2(2+h)}}}
{{{g(2+h)=(8+4h)+(8h+4h^2)+(2h^2+h^3)}}}
{{{g(2+h)=8+12h+6h^2+h^3}}}