Let's simplify the given expression step by step.
We start with the expression:
[tex]\[
-\left(4x^3 + x^2\right) + 2\left(x^3 - 3x^2\right)
\][/tex]
First, we'll distribute the negative sign inside the first parenthesis:
[tex]\[
-(4x^3 + x^2) = -4x^3 - x^2
\][/tex]
Next, we'll distribute the 2 inside the second parenthesis:
[tex]\[
2(x^3 - 3x^2) = 2x^3 - 6x^2
\][/tex]
Now, we combine the two results:
[tex]\[
-4x^3 - x^2 + 2x^3 - 6x^2
\][/tex]
To simplify, we'll combine the like terms. Group the [tex]\(x^3\)[/tex] terms together and the [tex]\(x^2\)[/tex] terms together:
[tex]\[
(-4x^3 + 2x^3) + (-x^2 - 6x^2)
\][/tex]
Compute the sums for each group of like terms:
[tex]\[
-4x^3 + 2x^3 = -2x^3
\][/tex]
[tex]\[
-x^2 - 6x^2 = -7x^2
\][/tex]
Therefore, the simplest form of the given expression is:
[tex]\[
-2x^3 - 7x^2
\][/tex]
So the correct answer is:
[tex]\[
\boxed{-2x^3 - 7x^2}
\][/tex]
Thus, the correct option is:
[tex]\[
\boxed{C}
\][/tex]
