यदि `1,omega,omega^(2)` इकाई के घनमूल है सिद्ध कीजिए कि
`(x-y)(xomega-y)(xomega^(2)-y)=x^(3)-y^(3)`

Explanation

बायाँ पक्ष `=(x-y)(xomega-y)(xomega^(2)-y)`
`=(x-y)(x^(2)omega^(3)-xyomega-xyomega^(2)+y^(2))`
`=(x-y)[x^(2)omega^(3)-(omega+(omega+omega^(2))xy+y^(2)]`
`=(x-y)[x^(2)*1-(-1)xy+y^(2)]" "[becauseomega^(3)=1,1+omega+omega^(2)=0]`
`=(x-y)(x^(2)+xy+y^(2))=x^(3)-y^(3)=` दायाँ पक्ष