Question

Suppose X and Y represent two different school populations where X > Y and X and Y must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary.
X2 Y2
X2 − Y2
2(X Y)
(X Y)2

Answer 1

Assuming the empty spaces are addition signs, the correct answer is:

(X+Y)²

Explanation:

X²+Y² would be greater than X²-Y² since addition gives a greater result than subtraction.

X²+Y² would be greater than 2(X+Y); this is because 2(X+Y) = 2X+2Y, which will be less than X²+Y², since X>Y.

(X+Y)² = (X+Y)(X+Y). This can be simplified using the distributive property:

X(X)+X(Y)+Y(X)+Y(Y) = X²+XY+YX+Y² = X²+2XY+Y². This is greater than X²+Y².