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. 2(a + b) (a + b)2 a2 + b2 a2 − b2

The first one is 
left at 2(A + B)

The second one is
A^2 + 2AB + B^2 The expanded version is greater than A^2 + B^2 See below for why.

(A + B)^2 / [2(A + B) ] = (A + B)/2 which is what is  left over when (A + B)^2 is divided by the first one.
 
(A + B)^2 / (A^2 - B^2) = (A + B) * (A + B) / [(A + B) (A - B)] = (A + B) / (A - B) which is less than (A + B)/2 for (A - B)>2

The third one is just A^2 + B^2 which is smaller than the second one by an amount equal to 2AB. Since A and B are both > 0, 2 AB must be > 0

A^2 - B^2