Answer
$F(a+h-F(a)=h^2+2ah+3h$
Work Step by Step
Combining the results of (a) and (b), then $F(a+h)-F(a)$ is equal to
\begin{array}{l}\require{cancel}
(a^2+2ah+h^2+3a+3h+2)-(a^2+3a+2)
\\\\=
a^2+2ah+h^2+3a+3h+2-a^2-3a-2
\\\\=
\cancel{(a^2-a^2)}+2ah+h^2+\cancel{(3a-3a)}+3h+\cancel{(2-2)}
\\\\=
h^2+2ah+3h
\end{array}
