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

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.