Factorise : `|{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|`

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

factorise: det[[x,y,zx^(2),y^(2),z^(2)yz,zx,xy]]

|[1/x,1/y,1/z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|

Show that: |[x, y ,z],[x^2, y^2, z^2], [yz, zx, xy ]|=(x-y)(y-z)(z-x).(xy+yz+zx)

The value of |{:(x,x^2-yz,1),(y,y^2-zx,1),(z,z^2-xy,1):}| is

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

proof |[x,y,z],[x^(2),y^(2),z^(2)],[yz,zx,xy]| = |[1,1,1],[x^(2),y^(2),z^(2)],[x^(3),y^(3),z^(3)]|