To simplify the expression [tex]\(-x(4x^2 - 6x + 1)\)[/tex], let’s follow these steps:
1. Distribute the [tex]\(-x\)[/tex] across each term inside the parentheses.
2. Carefully apply the distribution to each term.
Let’s proceed step-by-step:
1. Distribute [tex]\( -x \)[/tex] to the first term [tex]\( 4x^2 \)[/tex]:
[tex]\[
-x \cdot 4x^2 = -4x^3
\][/tex]
2. Distribute [tex]\( -x \)[/tex] to the second term [tex]\( -6x \)[/tex]:
[tex]\[
-x \cdot (-6x) = 6x^2
\][/tex]
3. Distribute [tex]\( -x \)[/tex] to the third term [tex]\( 1 \)[/tex]:
[tex]\[
-x \cdot 1 = -x
\][/tex]
Now, combine these distributed terms together:
[tex]\[
-4x^3 + 6x^2 - x
\][/tex]
So, the simplest form of the expression [tex]\(-x(4x^2 - 6x + 1)\)[/tex] is:
[tex]\[
x(-4x^2 + 6x - 1)
\][/tex]
Among the provided options, the correct answer is:
B. [tex]\(-4x^3 + 6x^2 - x\)[/tex]
