Question

if w is cube root of unity , then prove that

( x - y ) ( x w - y ) (x w 2 - y ) = x3 - y3

Answer 1

(x-y) (xw-y) (xw²-y)

= (x-y) (x²w³-xyw-xyw²+y²)

= (x-y) [x²+(1+w²)xy-xyw²+y²]

= (x-y) (x²+xy+xyw²-xyw²+y²)

= (x-y) (x²+xy+y²)

= x³-y³#

1+w+w²=0 , w³=1