Let's simplify the given expression step by step.
The expression to simplify is:
[tex]\[
-\left(4x^3 + x^2\right) + 2\left(x^3 - 3x^2\right)
\][/tex]
First, we distribute the negative sign and the 2 inside their respective parentheses.
1. Distribute the [tex]\(-1\)[/tex] in [tex]\(-\left(4x^3 + x^2\right)\)[/tex]:
[tex]\[
-1 \cdot 4x^3 + -1 \cdot x^2 = -4x^3 - x^2
\][/tex]
2. Distribute the [tex]\(2\)[/tex] in [tex]\(2\left(x^3 - 3x^2\right)\)[/tex]:
[tex]\[
2 \cdot x^3 + 2 \cdot (-3x^2) = 2x^3 - 6x^2
\][/tex]
Now, substitute these results back into the original expression:
[tex]\[
-4x^3 - x^2 + 2x^3 - 6x^2
\][/tex]
Next, combine the like terms (terms with [tex]\(x^3\)[/tex] and terms with [tex]\(x^2\)[/tex]):
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-4x^3 + 2x^3 = -2x^3
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-x^2 - 6x^2 = -7x^2
\][/tex]
So the simplified expression is:
[tex]\[
-2x^3 - 7x^2
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{-2 x^3 - 7 x^2}
\][/tex]
So the answer is B.
