Explanation

Let t = 1 + x + y; for positive x and y, t > 1, and t < t^2 holds for every t > 1 since t^2 - t = t(t-1) > 0. Hence 1 + x + y < (1 + x + y)^2 is always true. The other inequalities fail for small values (e.g., x = y = 1 gives 1 > 2 for (A), and x + y < 1 breaks (B) and (C)). Hence (D) is the universally true inequality.