Answer
a. $\quad-h(2x+h)$
b. $\quad-2x-h$
Work Step by Step
a.
$ f(x+h)=2-(x+h)^{2}=\quad$ ...square of a sum
$=2-(x^{2}+2xh+h^{2})$
$=2-x^{2}-2xh-h^{2}$
$f(x+h)-f(x)=2-x^{2}-2xh-h^{2}-(2-x^{2})$
$=2-x^{2}-2xh-h^{2}-2+x^{2}$
$=-2xh-h^{2}$
$=-h(2x+h)$
b.
using the result of (a),
$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{-h(2x+h)}{h}=\quad$ .. reduce h,
$=-(2x+h)$
$=-2x-h$
