## College Algebra (10th Edition)

$6x+3h$
$f(x)=3x^{2}+2$ $\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{3(x+h)^{2}+2-(3x^{2}+2)}{h}$ ... expand the square, $(a+b)^{2}=a^{2}+2ab+b^{2}$ $=\displaystyle \frac{3x^{2}+6xh+3h^{2}+2-3x^{2}-2}{h}$ ... simplify: the $x^{2}$ terms, and the constants cancel, $=\displaystyle \frac{6xh+3h^{2}}{h}$ ...factor out h $=\displaystyle \frac{h(6x+3h)}{h}$ ... h cancels $=6x+3h$