RBornPowerScore wrote:

If \(x\) is positive and \(-x < y < 0\), then which of the following must be negative?

A. \((x + y)^2\)

B. \((x - y)^2\)

C. \((y - x)^2\)

D. \(x^2 - y^2\)

E. \(y^2 - x^2\)

Amazing question.

Note : x is a positive number but negative x is greater than y, which is also negative. So, we can conclude that positive x is greater that the value of y.

Suppose ,

x = 10 and negative x = -10.

y = -5

Option E:

\(y^2 - x^2\) = (-5)^2 - ( 10)^2

= 25 -100

= -75

The best answer is E.