Answer
$-3a^3+12a^2+a+1$
Work Step by Step
Removing the grouping symbols, then the given expression, $
(3+5a+3a^2-a^3)-(2+4a-9a^2+2a^3)
$, is equivalent to
\begin{array}{l}
3+5a+3a^2-a^3-2-4a+9a^2-2a^3
.\end{array}
By combining like terms, then
\begin{array}{l}
(-a^3-2a^3)+(3a^2+9a^2)+(5a-4a)+(3-2)
\\\\=
-3a^3+12a^2+a+1
.\end{array}