`[[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)`

[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

By using properties of determinants.Show that: det[[x,x^(2),yzy,y^(2),zxz,z^(2),xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

xquad x ^ (2), y2yquad y ^ (2), 2xz, z ^ (2), xy] | = (xy) (yz) (zx) (xy + yz + 2x)

Determinant , form (x-y)(y-z)(z-x)(xy+yz+zx), of

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

Show that |[yz-x^2, zx-y^2, xy-y^2] , [zx-y^2, xy-z^2, yz-x^2] , [xy-z^2, yz-x^2, zx-y^2]|= |[r^2, u^2, u^2] , [u^2, r^2, u^2] , [u^2, u^2, r^2]| where r^2 = x^2+y^2+z^2 and u^2= xy+yz+zx

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

Simplify- (x-y)/(xy)+(y-z)/(yz)+(z-x)/(zx)

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]|