If $B > A$, then which expression will have the highest value (given that $A$ and $B$ are positive integers)?

### Concept & Strategy Comparing the magnitude of basic arithmetic expressions depends on the size of the integers $A$ and $B$. When integers are $1$ or greater, multiplication typically grows much faster than addition. ### Step-by-Step Solution * **Given:** $B > A$ and $A, B \in \mathbb{Z}^+$. * **Testing Values:** * Case 1: $A = 1, B = 2$ * $A - B = -1$ * $AB = 2$ * $A + B = 3$ (Here $A+B$ is greater) * Case 2: $A = 2, B = 3$ * $A - B = -1$ * $AB = 6$ * $A + B = 5$ (Here $AB$ is greater) * **Deduction:** The result is dependent on the specific values chosen. If $A=1$, the sum is larger. If $A \geq 2$, the product is larger. ### Exam Strategy & Shortcut Since there is no single expression that remains the largest for all possible positive integers $A$ and $B$, the answer must be "Can't say." Always test the edge case where $A=1$ for these types of "which is greatest" problems. ### Common Pitfall Assuming multiplication is always greater than addition. This is a common heuristic error; it only holds true for integers greater than $2$. ### Final Answer Therefore, the correct answer is **Can't say**.