|[x,y,z],[x^(2),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|=xyz(x-y)(y-z)(z-x)

Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z-x)dot

Prove that |[x,x^(2),x^(4)],[y,y^(2),y^(4)],[z,z^(2),z^(4)]|=xyz(x-y)(y-z)(z-x)(x+y+z)

Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3)):}|=|{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x)

Prove the following identities : |{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x) .

Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,y^2,y^3),(z,z^2,z^3)| = xyz(x-y(y-z)(z-x)

((x-y)^(3)+(y-z)^(3)+(z-x)^(3))/((x-y)(y-z)(z-x))=

Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

Prove that : Det[[x,x^2,x^3],[y,y^2,y^3],[z,z^2,z^3]]=xyz(x-y)(y-z)(z-x)

Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)