[" 3alffrin "32" arigs fro thring "],[qquad Delta=|[(y+z)^(2),xy,zx],[xy,(x+z)^(2),yz],[xz,yz,(x+y)^(2)]|=2xyz(x+y+z)^(3)]

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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 .

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

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

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

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

Show 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)

By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

xquad x ^ (2), y2yquad y ^ (2), 2xz, z ^ (2), xy] | = (xy) (yz) (zx) (xy + yz + 2x)