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.