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" if " |{:(yz-x^(2),,zx-y^(2),,xy-z^(2)...

`" 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

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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))

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

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

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

xy,xz,x^(2)+1y^(2)+!,yz,xyyz,z^(2)+1,xz]|=1+x^(2)+y^(2)+z^(2)

prove that: |(y^(2)z^(2),yz,y+z),(z^(2)x^(2),zx,z+x),(x^(2)y^(2),xy,x+y)|=0

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)