दिखाईए की सार्धिक `|{:(,(y+z)^(2),xy,zx),(,xu,(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: |[(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 |(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)

Factorise : |{:(x,y,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) .

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(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)

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