Sure, I'll show you how to subtract the given expressions step-by-step using a vertical format and simplify the answer completely.
You are given two expressions to subtract:
[tex]\[
\left(3y^2 - y + 2\right) - \left(-3 + 3y - 2y^2\right)
\][/tex]
First, it's helpful to align the expressions in a vertical format, keeping terms of the same degree in the same column:
[tex]\[
\begin{array}{r}
3y^2 - y + 2 \\
-(-2y^2 + 3y - 3) \\
\end{array}
\][/tex]
Next, distribute the negative sign across the second expression:
[tex]\[
\begin{array}{r}
3y^2 - y + 2 \\
-(-3 + 3y - 2y^2) \\
\end{array}
=
\begin{array}{r}
3y^2 - y + 2 \\
+ 2y^2 - 3y + 3 \\
\end{array}
\][/tex]
Now align and add the coefficients of like terms vertically:
[tex]\[
\begin{array}{r}
3y^2 - y + 2 \\
+ 2y^2 - 3y + 3 \\
\hline
5y^2 - 4y + 5 \\
\end{array}
\][/tex]
So, the expression simplifies to:
[tex]\[
5y^2 - 4y + 5
\][/tex]
Thus, the simplified form of the given subtraction problem is:
[tex]\[
5y^2 - 4y + 5
\][/tex]
