Step 1: Rule out products of squaring. The square of any real number (meaning any value on the number line) cannot be negative. Since squaring is the final operation in (A), (B), and (C), those answer choices must work out to either zero or some positive value.


✗A. $(x + y)^2$
✗B. $(x - y)^2$
✗C. $(y - x)^2$

Step 2: Assign values to x and y if you're unsure whether $x^2$ or $y^2$ is bigger. Neither x nor y is equal to zero, so both $x^2$ and $y^2$ are positive. If $x^2 > y^2$, then (E) must be correct, since a smaller positive minus a larger positive must equal a negative.

Let $x = 2$ and $y = -1$.
✗D. $2^2 - (-1)^2 = 4 - 1 = 3$
✓E. $(-1)^2 - 2^2 = 1 - 4 = -3$