D: (x+y)²
1) Gathering the data
X > Y
X >0
y>0
2) Since the point here is to find which expression shows the largest number of people, let's call arbitrarily each variable a number considering the constraints given x > y, and both x and y >0
x=100
y=81
A: x²+y² =(100)²+ (81)²=10000 +6561 = 16561
B: x² -y² = (x-y)(x+y) = (100-81)(100+81) = (19)(181) = 3439
C: 2(x+y) = 2 (100+81) = 2 (181)=362
D: (x+y)² = (100+81)² = 32761
3) So the largest expression to calculate these populations, is the square of the sum.
D: (x+y)²
