Question

(a-b) (a-bw) (a-bw^2) = a^3-b^3 complex root of unity show that​

Answer 1

Answer:

(a-b)(a-bw)(a-bw^2)

= (a^2-abw-ab+b^2w)(a-bw^2)

= a^3 - a^2bw - a^2b + ab^2w - a^2bw ^2 +ab^2w^3 + ab^2w^2 - b^3w^3

= a^3 - a^2b(1+w+w^2) +ab^2( w+w^3+w^2) - b^3w^3

since w is cube root of unity

w^3 = 1, 1+w+w^2 = 0

= a^3 - a^2b*0 + ab^2 (1+w+w^2) - b^3

= a^3 - 0 + 0 - b^3

= a^3 - b^3

proved

Answer 2

Answer:

sorry mujhe answer Nahin pata hai