Let's simplify the expression step-by-step:
Given expression:
[tex]\[
-x\left(4x^2 - 6x + 1\right)
\][/tex]
We will distribute the [tex]\(-x\)[/tex] to each term inside the parentheses:
Distribute [tex]\(-x\)[/tex] to [tex]\(4x^2\)[/tex]:
[tex]\[
-x \cdot 4x^2 = -4x^3
\][/tex]
Distribute [tex]\(-x\)[/tex] to [tex]\(-6x\)[/tex]:
[tex]\[
-x \cdot -6x = 6x^2
\][/tex]
Distribute [tex]\(-x\)[/tex] to [tex]\(1\)[/tex]:
[tex]\[
-x \cdot 1 = -x
\][/tex]
Putting all these together, we get:
[tex]\[
-4x^3 + 6x^2 - x
\][/tex]
So, the simplest form of the expression is:
[tex]\[
-4x^3 + 6x^2 - x
\][/tex]
Comparing this result with the given options, we find:
- A. [tex]\(-4 x^3 - 6 x^2 - x\)[/tex]
- B. [tex]\(-4 x^3 + 6 x^2 - x\)[/tex]
- C. [tex]\(-4 x^3 - 6 x + 1\)[/tex]
- D. [tex]\(-4 x^3 + 5 x\)[/tex]
The correct choice is:
[tex]\[
\boxed{-4 x^3 + 6 x^2 - x}
\][/tex]
Therefore, the answer is:
B. [tex]\(-4 x^3 + 6 x^2 - x\)[/tex]
So, the correct answer is:
[tex]\[
\boxed{B}
\][/tex]
