To find the simplest form of the given expression, [tex]$2x^3 + x^2 + 3(x^3 - 4x^2)$[/tex], let's simplify it step-by-step.
Given expression:
[tex]\[2x^3 + x^2 + 3(x^3 - 4x^2)\][/tex]
1. First, distribute the [tex]\(3\)[/tex] in the term [tex]\(3(x^3 - 4x^2)\)[/tex]:
[tex]\[3(x^3 - 4x^2) = 3x^3 - 12x^2\][/tex]
2. Substitute this back into the original expression:
[tex]\[2x^3 + x^2 + 3x^3 - 12x^2\][/tex]
3. Combine 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]\[x^2 - 12x^2 = -11x^2\][/tex]
4. So, the simplified form of the expression is:
[tex]\[5x^3 - 11x^2\][/tex]
Now, let's match this result with the given options:
A. [tex]\(5x^3 - 11x^2\)[/tex]
B. [tex]\(5x^3 - 3x^2\)[/tex]
C. [tex]\(3x^3 - 12x^2\)[/tex]
D. [tex]\(x^3 - 13x^2\)[/tex]
The correct answer is:
A. [tex]\(5x^3 - 11x^2\)[/tex]
