The correct answer is E

Explanation

The quantity (x + y)^2 can be expressed as (x^2) +2xy+ (y^2). If (x + y)^2 = (x^2) + (y^2), then 2xy = 0 and xy = 0. Since xy = 0, either x = 0 or y = 0 or both. Therefore, statement III must be true, but statement I, x = 0, is not always true. For statement II, you can write (x-y)^2 = (x^2)-(2xy) + y^2, and since x times y = 0, it follows that (x-y)^2 = (x^2) + (y^2). Therefore, both statements II and III must be true.