To simplify the expression [tex]\(-x(4x^2 - 6x + 1)\)[/tex], we need to distribute the [tex]\(-x\)[/tex] across each term within the parenthesis. Here are the steps to do that:
1. Multiply [tex]\(-x\)[/tex] with the first term [tex]\(4x^2\)[/tex]:
[tex]\[
-x \cdot 4x^2 = -4x^3
\][/tex]
2. Multiply [tex]\(-x\)[/tex] with the second term [tex]\(-6x\)[/tex]:
[tex]\[
-x \cdot -6x = 6x^2
\][/tex]
3. Multiply [tex]\(-x\)[/tex] with the third term [tex]\(1\)[/tex]:
[tex]\[
-x \cdot 1 = -x
\][/tex]
Now, combine the results of these multiplications:
[tex]\[
-4x^3 + 6x^2 - x
\][/tex]
Therefore, the simplest form of the given expression is:
[tex]\[
-4x^3 + 6x^2 - x
\][/tex]
We then look at the given options to determine which one matches our simplified expression:
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]
It is clear that option B matches our simplified expression [tex]\(-4x^3 + 6x^2 - x\)[/tex]. Therefore, the correct answer is:
B. [tex]\(-4x^3 + 6x^2 - x\)[/tex]
