Prove that `(a+b)(a omega+b omega^(2))(a omega^(2)+b omega)=a^(3)+b^(3)`

(a+b omega+c omega^(2))(a+b omega^(2)+c omega)

omega is an imaginary root of unity.Prove that (a+b omega+c omega^(2))^(3)+(a+b omega^(2)+c omega)^(3)=(2a-b-c)(2b-a-c)(2c-a-b)

(a+b)^(2)+(a omega+b omega^(2))^(2)+(a omega^(2)+b omega)^(2)=

(a+b) (a omega+b omega^(2)) (aw^(2)+bw) =?

(a+omega b+omega^(2)c)(a+omega^(2)b+omega c)=a^(2)+b^(2)+c^(2)-ab-bc-ca

If a+b+c=0 and omega,omega^(2) are imaginary cube roots of unity,then (a+b omega+c omega^(2))^(2)+(a+b omega^(2)+c omega)^(3)=3abc (b) 6abc (c) 9 abc (d) 27 abc

Let omega be a complex cube root of unity with 0