The question is: find f(x+h) for each

and the function given is f(x)=x^3+x

after you turn it into f(x+h)=(x+h)^3+(x+h) how do you multiply out the cube?

Take some time to memorize the identities below which may be useful for your academic career:

(a+b)^3=(a^3+3a^2b+3ab^2+b^3) ...(1)
(a-b)^3=(a^3-3a^2b+3ab^2-b^3) ...(2)

Substitute x for a, and h for b in (1) above to get (x+h)^3.