To find the simplest form of the expression [tex]\(-\left(2x^3 + x^2\right) + 3\left(x^3 - 4x^2\right)\)[/tex], we need to follow these steps:
1. Distribute the negative sign and the 3 across the terms within the parentheses:
- For [tex]\(-\left(2x^3 + x^2\right)\)[/tex]:
[tex]\[
-2x^3 - x^2
\][/tex]
- For [tex]\(3\left(x^3 - 4x^2\right)\)[/tex]:
[tex]\[
3x^3 - 12x^2
\][/tex]
2. Combine the expressions obtained from the distribution step:
[tex]\[
-2x^3 - x^2 + 3x^3 - 12x^2
\][/tex]
3. Group the like terms, which are the terms involving [tex]\(x^3\)[/tex] and the terms involving [tex]\(x^2\)[/tex]:
[tex]\[
(-2x^3 + 3x^3) + (-x^2 - 12x^2)
\][/tex]
4. Combine the coefficients of the like terms to simplify:
[tex]\[
1x^3 - 13x^2
\][/tex]
5. Rewrite in the simplest form:
[tex]\[
x^3 - 13x^2
\][/tex]
Thus, the simplest form of the expression is:
[tex]\[
x^3 - 13x^2
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{C. \; x^3 - 13x^2}
\][/tex]
