Verified answer

Answer:

x² + y² + z² + 2xy + 2xz + 2yz = 0

Step-by-step explanation:

(x + y + z)² = 0

(x*x) + (x*y) + (x*z) + (y*x) + (y*y) + (y*z) + (z*x) + (z*y) + (z*z) = 0

x² + xy + xz + xy + y² + yz + xz + yz + z² = 0

arrange

x² + y² + z² + xy + xy +xz + xz + yz + yz = 0

combine like terms

x² + y² + z² + 2xy + 2xz + 2yz = 0