Explanation

Since x + y + z = 0, we have y + z = −x, z + x = −y and x + y = −z. The expression becomes x·x² + y·y² + z·z² = x³ + y³ + z³. By the identity x³ + y³ + z³ = 3xyz whenever x + y + z = 0, the value is 3xyz, option C.