Polynomial identity or factoring to simplify a given expression
The question requires using a polynomial identity (e.g., sum of cubes, difference of squares) or factoring a polynomial expression given an algebraic constraint to arrive at a simplified result.
Let x and y be real numbers such that $$\begin{aligned}
& x ^ { 3 } - 3 x ^ { 2 } y = 3 \\
& y ^ { 3 } - 3 x y ^ { 2 } = 11
\end{aligned}$$ Accordingly, what is the difference $x - y$? A) 3 B) 2 C) 1 D) - 2 E) - 3