Average rate of change for $f (x) = 2x^2 + 1$ on $[x, x + h]$

Question

I am trying to answer a question from the OpenStax Precalculus book. The question is #9, section 1.3, pdf page 48.

My calculation is:

$$\frac{(2x^2+2h^2+1)-(2x^2+1)}{(x + h) – (x)}$$

Giving $2h$.

However, the book says the answer is $4x + 2h$ and I cannot see what I am doing wrong.

Answer 1

It is $$\frac{2(x+h)^2+1-2x^2-1}{h}=\frac{2x^2+4xh+2h^2-2x^2}{h}$$