Sure! Let's set up the subtraction of the two polynomials in a vertical format and work through it step-by-step.
We need to subtract \( -4 + 3a^2 \) from \( 7a - a^2 \).
First, let's write the polynomials in a standard form and stack them vertically:
[tex]\[
\begin{array}{r}
7a - a^2 \\
-( - 4 + 3a^2) \\
\end{array}
\][/tex]
When we subtract polynomials, we change the sign of all the terms in the polynomial being subtracted and then combine like terms. Therefore:
Original:
[tex]\[
7a - a^2
\][/tex]
Subtracting \(-4 + 3a^2\):
[tex]\[
-( - 4 + 3a^2 ) = 4 - 3a^2
\][/tex]
Now, line up and change the signs:
[tex]\[
\begin{array}{r}
7a - a^2 \\
4 - 3a^2 \\
\end{array}
\][/tex]
Combine like terms:
[tex]\[
\begin{array}{r}
- a^2 - 3a^2 + 7a + 4 \\
= -4a^2 + 7a + 4
\end{array}
\][/tex]
So, the result of subtracting \(-4 + 3a^2\) from \(7a - a^2\) is:
[tex]\[
-4a^2 + 7a + 4
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{-4a^2 + 7a + 4}
\][/tex]
