`(x+omegay)(x+omega^2y) = (x^2-xy+y^2)`

If omega is a complex cube root of unity,then (x-y)(x omega-y)(x omega^(2)-y)=

(x omega ^ (2) + y omega + z) / (x omega + y + omega ^ (2)) = ((x omega + y + z omega ^ (2)) / (x omega ^ (2) + and omega + z)) ^ (2)

What should be added to product of (x ^(2) + xy - y ^(2)) and (x ^(2) - xy + y ^(2)) to get x ^(2) y ^(2)

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

If x = sin alpha + sin beta, y = cos alpha + cos beta then tan alpha + tan beta = (1) (8xy) / (2 (y ^ 2-x ^ 2) + (x ^ 2 + y ^ 2 ) (x ^ 2 + y ^ 2-2)) (2) (4xy) / ((y ^ 2-x ^ 2) + (x ^ 2 + y ^ 2) (x ^ 2 + y ^ 2-2 )) (3) (8xy) / ((x ^ 2 + y ^ 2) (x ^ 2 + y ^ 2-2)) (4) 4xy

Multiply (x^2+xy+y^2) by (x^2-xy+y^2) , check the answer , if x=2 , y=1