Which of the following is a cyclic expression?

Correct answer: b x² + y² + z² − 2xyz

In x² + y² + z² − 2xyz, cycling gives y² + z² + x² − 2yzx, the same; it is cyclic even though it is not homogeneous.

Why the other options are wrong

• a x³ + y³ + z³ + 3x²yz: In x³ + y³ + z³ + 3x²yz, cycling turns the last term into 3y²zx, so the expression changes.
• c 3x²y + 2y²z + z²x: In 3x²y + 2y²z + z²x, cycling gives 3y²z + 2z²x + x²y; the unequal coefficients make it change.
• d x² − y² + z²: In x² − y² + z², cycling gives y² − z² + x², which is different.