Answer:
The largest possible product of two positive integers whose sum is 9 is achieved when the two integers are as far apart as possible, which occurs when one integer is the largest possible integer and the other is the smallest possible integer. The largest possible integer is the one that is closest to but less than 9, which is 8, and the smallest possible integer is 1. The product of 8 and 1 is 8, so the largest possible product of two positive integers whose sum is 9 is 8.