Find the difference quotient and simplify your answer: f(x)=x^3 + 3x, f(x+h) - f(x)/h, h is not equal to zero

Question

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Show work.

1.When you FOIL (x+h)^3 what do you get?

2. Secondly, the book is showing the answer as "3x^2 + 3xh +h^2 + 3"

Answer 1

f(x)=x^3 + 3x
f(x+h) - f(x)/h =
(x+h)^3 +3(x+h) - (x+h)/h =
x^3 + 3x^2h + 3xh^2 + h^3 + 3x + 3h - xh^-1 - 1