Questions on Algebra: Polynomials, rational expressions and equations answered by real tutors!

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Question 152517: g(2+h)=x to the third
the instructor gave us x=(2+h)
and the answer 8+12h+6h suared+h to the third
i haven't been able to get that as my answer.
here's what I have done:
g(2+h)=x to the third
g=(2+h)to the third
g=(2+h)(2+h)(2+h)
g=4+2h+2h+hsquared(2+h)
g=8+4h+4h+2h+2h+2hsquared+h to the third
g=8+12h+2hsquared+h to the third: g(2+h)=x to the third
the instructor gave us x=(2+h)
and the answer 8+12h+6h suared+h to the third
i haven't been able to get that as my answer.
here's what I have done:
g(2+h)=x to the third
g=(2+h)to the third
g=(2+h)(2+h)(2+h)
g=4+2h+2h+hsquared(2+h)
g=8+4h+4h+2h+2h+2hsquared+h to the third
g=8+12h+2hsquared+h to the third
Answer by Fombitz(1740) About Me  (Show Source):
You can put this solution on YOUR website!
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