"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.

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"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.

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

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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
Ok, thank you Just needed some verification
you're welcome

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