Let's simplify the given expression step-by-step:
Given the expression:
[tex]\[ 3\left[\left(x^3 - 7x + 1\right) - \left(x + 4\right)\right] \][/tex]
First, distribute the subtraction inside the brackets:
[tex]\[ \left(x^3 - 7x + 1\right) - \left(x + 4\right) = x^3 - 7x + 1 - x - 4 \][/tex]
Combine like terms:
[tex]\[ x^3 - 7x - x + 1 - 4 = x^3 - 8x - 3 \][/tex]
Now, multiply through by 3:
[tex]\[ 3 \left(x^3 - 8x - 3\right) = 3x^3 - 24x - 9 \][/tex]
Thus, the simplified form of the expression is:
[tex]\[ 3x^3 - 24x - 9 \][/tex]
Looking at the given multiple-choice options:
A. [tex]\( 3x^3 - 24x - 9 \)[/tex]
B. [tex]\( 3x^3 - 5x - 6 \)[/tex]
C. [tex]\( x^3 - 8x - 3 \)[/tex]
D. [tex]\( 3x^3 - 6x + 15 \)[/tex]
The correct answer is:
A. [tex]\( 3x^3 - 24x - 9 \)[/tex]
