" Prove that "|[x,y,z],[x^(2),y^(2),z^(2)],[yz,zx,xy]|=(y-z)(z-x)(x-1)

|[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)

By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

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

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)]|

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

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]|

Prove that |[1,x,x^2-yz],[1,y,y^2-zx],[1,z,z^2-xy]|= 0

Prove that |(x,x^2,yz),(y,y^2,zx),(z,z^2,xy)|= (x-y)(y-z)(z-x)(xy + yz + zx) .

Using the properties of determinants, show that : |[[x^2, y^2, z^2],[yz, zx, xy],[x,y,z]]|= (x-y)(y-z)(z-x)(xy+yz+zx) .