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

A. [tex]x^3 - 3x^2[/tex]
B. [tex]5x^3 - 12x^2[/tex]
C. [tex]x^3 - 13x^2[/tex]
D. [tex]5x^3 - 11x^2[/tex]



Answer :

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]