Question

which expression means \the cube of the difference between a number and 4\?
○ ( x^3 - 4 )
○ ( (x - 4)^3 )
○ ( (4 - x)^3 )
○ ( x - 4^3 )

Explanation:

Step1: Analyze "difference between a number and 4"

Let the number be \( x \). The difference between \( x \) and 4 is \( x - 4 \).

Step2: Analyze "the cube of the difference"

To find the cube of \( x - 4 \), we raise \( x - 4 \) to the power of 3, which is \( (x - 4)^3 \).
Now let's check the other options:

• \( x^3 - 4 \): This is the cube of the number minus 4, not the cube of the difference.
• \( (4 - x)^3 \): This is the cube of the difference between 4 and the number (which is the negative of the difference between the number and 4, but the problem says "the difference between a number and 4", so the order is number - 4).
• \( x - 4^3 \): This is the number minus the cube of 4, not the cube of the difference.

Answer:

B. \((x - 4)^3\)