Which of the following must be negative whenever x>y>0?

A) x^2 -4xy + y^2

B) x^2 -2xy – y^2

C) x^2 – xy -2y^2

D) y^2 -x^2 -xy

E) y^2 -x^2 +xy

First, get rid of (A) and (E) because they have + signs in them. Those aren’t gonna work.

Now look at what you have left. Can you factor any of those in a useful way?

Hmm…(D) has a difference of two squares in it.

If *x* is bigger than *y*, then *y – x* is always going to be negative. Since *x* and *y* are both positive, *y + x* will always be positive, and *xy* will always be positive. Negative times positive is always negative, so is always (positive)(negative) – positive. That’s always going to be negative.