Without expanding, prove the following
`|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,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]]|= xyz (x-y)(y-z)(z-x)

Without expanding, prove the following |(y+z,z,y),(z,z+x,x),(y,x,x+y)|=4xyz

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}| = (x-y)(y-z)(z-x)(x+y+z) .

Show that |(1,x^2,x^3),(1,y^2,y^3),(1,z^2,z^3)| = (x-y),(y-z)(z-x)(xy+yz+zx)

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: {:|(1,x,x^3),(1,y,y^3),(1,z,z^3)| = (x-y)(y-z)(z-x)(x+y+z)

Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x , y),(1,1,1):} = 0

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)