Answer
a. $x^{2}+2xh+h^{2}-3$
b. $2xh+h^{2}$
c. $2x+h$
Work Step by Step
$f(x)=x^{2}-3$
a.
$f(x+h)=(x+h)^{2}-3=(x^{2}+2xh+h^{2})-3$
$=x^{2}+2xh+h^{2}-3$
b.
$f(x+h)-f(x)$
$=(x^{2}+2xh+h^{2}-3)-(x^{2}-3)$
$=x^{2}+2xh+h^{2}-3-x^{2}+3$
$=2xh+h^{2}$
c.
$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{2xh+h^{2}}{h}=\frac{h(2x+h)}{h}$
$=2x+h$
