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

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

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 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)

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

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

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

Using properties of determinants,prove that [[-yz,y^(2)+yz,z^(2)+yzx^(2)+xz,-xz,z^(2)+xyx^(2)+xy,y^(2)+xy,-xy]]=(xy+yz+zx)^(2)