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

Explanation

`L.H.S.=xyz=(a+b)(aomega+bomega^2)(a omega^2+b omega)`
`=(a+b)(a^2omega^3+abomega^2+abomega^4+b^2omega^3)`
`=(a+b){a^2+b^2+ab(omega^2+omega)}`
`=(a+b){a^2-b^2+ab(omega^2=omega)}`
`=(a+b)(a^2-ab+b^2)=a^3+b^3="R.H.S.(Proved)"`