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

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

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

Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2x y z(x+y+z)^3 .

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

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

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.

Which of the following are possible solutions of |(y^2+z^2,xy,xz),(xy,z^2+x^2,yz),(zx,zy,x^2+y^2)|=8 are (x,y,z)=

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