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."


A. X^2 + Y^2
B. X^2 − Y^2
C. 2(X + Y)
D. (X + Y)^2

I'm a little confused on this question. I need someone to help me understand how to solve it rather than just telling me the answer.

Answer 1

One way to do this is to replace x and y with numeric values (eg: x = 15 and y = 10) and see which expression is the largest

Answer 2

Another way is to realize that if x is some positive number, then x^2 is some larger positive number. Same for y

So x^2 + y^2 is certainly going to be larger than x+y

x^2 + y^2 is going to be larger than x^2 - y^2 because subtracting off the y^2 term makes the second result smaller.

hopefully this is making sense?

Answer 3

My first thought was that it would be D, is that correct?

Answer 4

yes because (x+y)^2 expands out to x^2 + 2xy + y^2

it's larger than x^2 + y^2 because of that extra 2xy added on

Answer 5

Ok, thank you
Just needed some verification

Answer 6

you're welcome