`" if " |{:(yz-x^(2),,zx-y^(2),,xy-z^(2)),(xz-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)):}|` then

(x-y-z)^(2)-(x^(2)+y^(2)+z^(2))=2(yz-zx-xy)

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

(y^(2)+yz+z^(2))/((x-y)(x-z))+(z^(2)+zx+x^(2))/((y-z)(y-x))+(x^(2)+xy+y^(2))/((z-x)(z-y))

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

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

(y^(2)+yz+z^(2))/((x-y)(x-z)) + (z^(2)+zx+x^(2))/((y-z)(y-x)) + (x^(2)+xy+y^(2))/((z-x)(z-y))

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.

If |y z-x^2z x-y^2x y-z^2x z-y^2x y-z^2y z-x^2x y-z^2y z-x^2z x-y^2|=|r^2u^2u^2u^2r^2u^2u^2u^2r^2| , where r^2=x^2+y^2+z^2 & u^2= x y + y z+z x