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Which expression is the simplest form of [tex]-\left(3x^3 + x^2\right) + 2\left(x^3 - 4x^2\right)[/tex]?

A. [tex]-x^3 - 9x^2[/tex]

B. [tex]-x^3 - 3x^2[/tex]

C. [tex]5x^3 - 8x^2[/tex]

D. [tex]5x^3 - 7x^2[/tex]


Sagot :

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]