Select the correct answer.

What is the simplest form of this expression?
[tex]\[ -x\left(4x^2 - 6x + 1\right) \][/tex]

A. [tex]\(-4x^3 - 6x^2 - x\)[/tex]
B. [tex]\(-4x^3 + 6x^2 - x\)[/tex]
C. [tex]\(-4x^3 - 6x + 1\)[/tex]
D. [tex]\(-4x^3 + 5x\)[/tex]



Answer :

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]