Question

If 1, w, w^2 are the cube roots of unity, then prove (x-y)(xw-y)(xw^2-y)=x^3-y^3

Answer 1

I have your answer

just only put formula and your

Answer 2

Answer:

Step-by-step explanation:

L.H.S.

 ( x - y ) ( xw - y ) ( xw^2 - y )

= ( x - y ) [ ( xw - y ) ( xw^2 - y) ]

= ( x - y ) (x^2w^3 - xyw - xyw^2 + y^2 )

= ( x - y ) ( x^2(1) - xy ( w + w^2 ) + y^2 )     ( because w^3=1)

= ( x - y ) ( x ^2 - xy ( -1 ) + y^2 )  ( because 1 + w + w^2=0 => w + w^2 = -1 )

= ( x - y ) ( x^2 + y^2 + xy )

= x^3 + y^3           ( because (x^3 + y^3) = ( x - y ) ( x^2 + y^2 + xy )

= R.H.S.

                      Hence , proved.