To find the simplest form of [tex]\(-\left(3 x^3 + x^2\right) + 2\left(x^3 - 4 x^2\right)\)[/tex], let's go through the expression step-by-step.
1. Expand Each Part of the Expression:
- The first term is [tex]\(-\left(3 x^3 + x^2\right)\)[/tex]. Distributing the negative sign, we get:
[tex]\[
-3 x^3 - x^2
\][/tex]
- The second term is [tex]\(2\left(x^3 - 4 x^2\right)\)[/tex]. Distributing the 2, we get:
[tex]\[
2 x^3 - 8 x^2
\][/tex]
2. Combine Like Terms:
Now, combine the like terms from the expanded forms. Group the [tex]\(x^3\)[/tex] terms together and the [tex]\(x^2\)[/tex] terms together:
[tex]\[
(-3 x^3) + (2 x^3) + (-x^2) + (-8 x^2)
\][/tex]
3. Simplify the Expression:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-3 x^3 + 2 x^3 = -x^3
\][/tex]
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-x^2 - 8 x^2 = -9 x^2
\][/tex]
Putting these together, the simplified form of the given expression is:
[tex]\[
-x^3 - 9 x^2
\][/tex]
Therefore, the simplest form of [tex]\(-\left(3 x^3 + x^2\right) + 2\left(x^3 - 4 x^2\right)\)[/tex] is [tex]\(-x^3 - 9 x^2\)[/tex], which corresponds to option A.
So, the correct answer is:
A. [tex]\(-x^3 - 9 x^2\)[/tex]
