Question

Suppose A and B represent two different school populations where A > B and A and B must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary.
A: 2(A + B)
B: (A + B)2
C: A2 + B2
D: A2 − B2

Answer 1

A+B)^2 is the largest.  It is A^2+2AB+B^2, which is clearly greater than the last two options.  To compare (A+B)^2 and 2(A+B), we remove one A+B so that we're just comparing A+B and 2.  As A+B must be at least 3 (as both must be positive integers, and one must be greater than the other, leading to a minimum value of A=2, B=1), A+B is greater than 2, and as a result, (A+B)^2 is always the largest.