Final answer:
To find the expression that is a multiple of 12, we need to analyze the given options. Option A (ab) is the only expression that is guaranteed to be a multiple of 12.
Step-by-step explanation:
To determine which expression is a multiple of 12, we need to look for the expression that can be divided evenly by 12. Let's analyze the given options:
A) (ab) only: Since both a and b are multiples of 3 and 4 respectively, their product ab will also be divisible by 12, making this option a multiple of 12.
B) (3a + 4b) only: This expression can be simplified to 3a + 4b, which is not necessarily divisible by 12. Therefore, this option is not a multiple of 12.
C) (4a + 3b) only: Similar to option B, this expression can be simplified to 4a + 3b, which is not necessarily divisible by 12. So, this option is not a multiple of 12.
D) (ab) and (3a + 4b): We already established that (ab) is a multiple of 12. However, (3a + 4b) may or may not be divisible by 12. Therefore, this option is not guaranteed to be a multiple of 12.
E) (ab) and (4a + 3b): Similar to option D, (ab) is a multiple of 12. And (4a + 3b) may or may not be divisible by 12. So, this option is also not guaranteed to be a multiple of 12.
Based on our analysis, only option A (ab) is guaranteed to be a multiple of 12.