Answer
$g(a+h)-g(a)=h^2+2ah+2h$
Work Step by Step
Using the results of (a) and (b), then $g(a+h)-g(a)$ is equal to
\begin{array}{l}\require{cancel}
a^2+2ah+h^2+2a+2h+1-(a^2+2a+1)
\\\\=
a^2+2ah+h^2+2a+2h+1-a^2-2a-1
\\\\=
\cancel{a^2}+2ah+h^2+\cancel{2a}+2h+\cancel{1}-
\cancel{a^2}-\cancel{2a}-\cancel{1}
\\\\=
h^2+2ah+2h
.\end{array}
