To find the simplest form of the expression [tex]\( -\left(2 x^3 + x^2\right) + 3\left(x^3 - 4 x^2\right) \)[/tex], we need to follow these steps:
1. Distribute the negative sign and the 3:
- For the first part, distribute the negative sign:
[tex]\[
- (2 x^3 + x^2) = -2 x^3 - x^2
\][/tex]
- For the second part, distribute the 3:
[tex]\[
3(x^3 - 4 x^2) = 3 x^3 - 12 x^2
\][/tex]
2. Combine like terms:
[tex]\[
-2 x^3 - x^2 + 3 x^3 - 12 x^2
\][/tex]
To combine, group the terms with the same powers of [tex]\( x \)[/tex]:
[tex]\[
(-2 x^3 + 3 x^3) + (-x^2 - 12 x^2)
\][/tex]
3. Simplify the coefficients:
- For [tex]\( x^3 \)[/tex] terms: [tex]\( -2 x^3 + 3 x^3 = x^3 \)[/tex]
- For [tex]\( x^2 \)[/tex] terms: [tex]\( -x^2 - 12 x^2 = -13 x^2 \)[/tex]
So, the simplified expression is:
[tex]\[
x^3 - 13 x^2
\][/tex]
Therefore, the simplest form of the given expression [tex]\( -\left(2 x^3 + x^2\right) + 3\left(x^3 - 4 x^2\right) \)[/tex] is [tex]\( x^3 - 13 x^2 \)[/tex].
The correct answer is:
[tex]\[
\boxed{C. \ x^3 - 13 x^2}
\][/tex]
