Let's simplify the given expression step by step:
The given expression is [tex]\( 2x^3 - x^2 + 3(x^3 - 4x^2) \)[/tex].
First, distribute the [tex]\(3\)[/tex] inside the parentheses:
[tex]\[ 2x^3 - x^2 + 3(x^3) + 3(-4x^2) \][/tex]
This simplifies to:
[tex]\[ 2x^3 - x^2 + 3x^3 - 12x^2 \][/tex]
Next, combine the like terms:
- Combine the [tex]\( x^3 \)[/tex] terms: [tex]\( 2x^3 + 3x^3 = 5x^3 \)[/tex].
- Combine the [tex]\( x^2 \)[/tex] terms: [tex]\( -x^2 - 12x^2 = -13x^2 \)[/tex].
So, the expression simplifies to:
[tex]\[ 5x^3 - 13x^2 \][/tex]
Now, we need to verify which of the given options matches this simplified expression.
A. [tex]\( x^3 - 13x^2 \)[/tex]
B. [tex]\( 5x^3 - 13x^2 \)[/tex]
C. [tex]\( 5x^3 - 5x^2 \)[/tex]
D. [tex]\( 3x^3 - 12x^2 \)[/tex]
From the simplification, we see that the correct simplified form is [tex]\( 5x^3 - 13x^2 \)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{\text{B. } 5x^3 - 13x^2} \][/tex]
