6(x+h)^3 how to factor this

Question

Question is actually algebra 2, but Ive forgotten how to factor this. The context is finding the difference quotient. F(X) = 6x^3, after plugging in (x+h) in the x spot we have 6(x+h)^3, this then needs to be subtracted from -(6x^3) over H. I dont understand how to simplify and cancel things out. I though factoring would help 

Answer 1

Steve:

 

I do not understand the question, as this is already factored. The only thing you could do is expand it by writing 6(X+h)(X+h)(X+h). There is no other change you could make while staying in factored form. If you multiply out this will leave factored form and enter a standard polynomial form.

Answer 2

the difference quotient   is     f(x+h) -f(x)

                                          --------------

                                               h

 6(x+h)^3 - 6x^3               6(x^3 +3x^2h + 3xh^2 + h^3) - 6x^3            18x^2h  + 18xh^2  + 6h^3

----------------------    =     ----------------------------------------------  =     ----------------------------------   =

              h                                                h                                                              h

 

18x^2   + 18xh  + 6h^2