Let's analyze the expression \( (9 - 5) \cdot 2 \).
First, we evaluate the expression inside the parentheses: \[ 9 - 5 = 4. \]
Next, we multiply the result by 2: \[ 4 \cdot 2 = 8. \]
Based on the evaluation, here’s the breakdown for each option you provided:
A. First cube each term \( 9^3 - 5^3 \) then subtract \( 729 - 125 = 604 \), and then multiply \( 604 \cdot 3 = 1,208 \).
- This is not correct for the expression \( (9 - 5) \cdot 2 \).
B. First subtract \( 9 - 5 = 4 \), then multiply \( 4 \cdot 2 = 8 \), and then cube \( 8^3 = 512 \).
- The first two steps are correct, but cubing the result is not part of solving \( (9-5) \cdot 2 \).
C. First cube each term \( 9^3 - 5^3 \) then multiply the second term \( 125 \cdot 2 = 250 \), and then subtract \( 729 - 250 = 479 \).
- This is also not correct for the expression \( (9 - 5) \cdot 2 \).
D. First subtract \( 9 - 5 = 4 \), then cube \( 4^3 = 64\), and then multiply \( 64 \cdot 2 = 128 \).
- Here, the first step is correct, but cubing and then multiplying is not appropriate for the expression.
The correct evaluation of the expression \( (9 - 5) \cdot 2 \) yields \( 8\), and none of the given options correctly solve \( (9-5) \cdot 2 \) as presented. The correct answer based on the steps provided is:
- First \( 9 - 5 = 4 \), then \( 4 \cdot 2 = 8 \).
Thus, none of the answer choices (A, B, C, D) are correct based on the intended operation of \( (9 - 5) \cdot 2 \).