If `x=a+b, y=a omega+b omega^2,z=a omega^2+bomega` show that`x^3+y^3+z^3=3(a^3+b^3)`

Explanation

`L.H.S.=x^3+y^3+z^3`
`(a+b)^3+(aomega+bomega^2)^3+(aomega^2+b^2)^3`
`a^3+3a^2b+3ab^2+b^3+a^3omega^3+3a^2b^2bomega^2+3aomegab^2omega^4+b^3omega^6+a^3omega^6+3a^2omega^4bomega+3aomega^2b^2omega^2+b^3omega^3`
`=a^3+a^3+a^3+b^3+b^3+b^3+3a^2b(1+omega^4+omega^5)+3ab^2(1+omega^5+omega^4)`
`3a^3+3b^3+0+0=3(a^3+b^3)="R.H.S.(Proved)"`