If x+y+z=0 show that

x+y+z=3xyz

Step-by-step explanation:

perhaps you mean

x^3+y^3+z^3 = 3xyz

because

x+y+z = 0

x^3 + y^3 + z^3 - 3xyz = (x + y + z) (x^2 + y^2 + z^2 - xy - yz - xz)

(this equation is an identity)

x^3 + y^3 + z^3 - 3xyz = (x + y + z) (x^2 + y^2 + z^2 - xy - yz - xz)

x^3 + y^3 + z^3 - 3xyz = (0) (x^2 + y^2 + z^2 - xy - yz - xz)

x^3 + y^3 + z^3 - 3xyz = 0

x^3 + y^3 + z^3 = 3xyz