Prove that `|[yz-x^2,zx-y^2,xy-z^2],[zx-y^2,xy-z^2,yz-x^2],[xy-z^2,yz-x^2,zx-y^2]|` is divisible by `(x+y+z),` and hence find the quotient.

yz-x^(2)quad zx-y^(2)quad xy-z^(2)| Prove that det[[yz-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]] is divisible by (x+y+z), and hence find the quotient.

Prove that quad det ([yx-x^(2),zx-y^(2),xy-z^(2)zx-y^(2),xy-z^(2),yz-x^(2)xy-z^(2),yz-x^(2),zx-y^(2)]) is divisible by (x+y+z) and hence find the quotient.

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

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

|(x^(2),y^(2)+z^(2),yz),(y^(2),z^(2)+x^(2),zx),(z^(2),x^(2)+y^(2),xy)| is divisible by

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

Show that: |[(y+z)^2, xy, zx],[xy, (x+z)^2, yz], [xz, yz, (x+y)^2]|=2xyz(x+y+z)^3

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