Answer :
To find the simplest form of the given expression \(-\left(2 x^3+x^2\right)+3\left(x^3-4 x^2\right)\), let's follow the steps one by one:
### Step 1: Distribute the Negative Sign and the Multiplication
Start by distributing the negative sign into the first parentheses and distributing the 3 into the second parentheses.
[tex]\[ -\left(2 x^3 + x^2\right) \implies -2 x^3 - x^2 \][/tex]
[tex]\[ 3\left(x^3 - 4 x^2\right) \implies 3 x^3 - 12 x^2 \][/tex]
### Step 2: Combine the Results
Now, combine the terms from both expressions.
[tex]\[ -2 x^3 - x^2 + 3 x^3 - 12 x^2 \][/tex]
### Step 3: Combine Like Terms
Combine the \(x^3\) terms and the \(x^2\) terms separately.
[tex]\[ (-2 x^3 + 3 x^3) + (- x^2 - 12 x^2) \][/tex]
[tex]\[ (3 x^3 - 2 x^3) + (- x^2 - 12 x^2) \][/tex]
[tex]\[ x^3 - 13 x^2 \][/tex]
### Conclusion
Hence, the simplest form of the expression \(-\left(2 x^3 + x^2 \right) + 3\left(x^3 - 4 x^2\right)\) is:
[tex]\[ x^3 - 13 x^2 \][/tex]
Therefore, the correct answer is:
C. [tex]\(x^3 - 13 x^2\)[/tex]
### Step 1: Distribute the Negative Sign and the Multiplication
Start by distributing the negative sign into the first parentheses and distributing the 3 into the second parentheses.
[tex]\[ -\left(2 x^3 + x^2\right) \implies -2 x^3 - x^2 \][/tex]
[tex]\[ 3\left(x^3 - 4 x^2\right) \implies 3 x^3 - 12 x^2 \][/tex]
### Step 2: Combine the Results
Now, combine the terms from both expressions.
[tex]\[ -2 x^3 - x^2 + 3 x^3 - 12 x^2 \][/tex]
### Step 3: Combine Like Terms
Combine the \(x^3\) terms and the \(x^2\) terms separately.
[tex]\[ (-2 x^3 + 3 x^3) + (- x^2 - 12 x^2) \][/tex]
[tex]\[ (3 x^3 - 2 x^3) + (- x^2 - 12 x^2) \][/tex]
[tex]\[ x^3 - 13 x^2 \][/tex]
### Conclusion
Hence, the simplest form of the expression \(-\left(2 x^3 + x^2 \right) + 3\left(x^3 - 4 x^2\right)\) is:
[tex]\[ x^3 - 13 x^2 \][/tex]
Therefore, the correct answer is:
C. [tex]\(x^3 - 13 x^2\)[/tex]
