Prove that `|(x,x^2,yz),(y,y^2,zx),(z,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, 4, y+z),(y, 4, z+x),(z, 4, x+y)|=

Prove that |{:(,x+y+2z,x,y),(,z,y+z+2z,y),(,z,x,z+x+2y):}|=2(x+y+z)^(3) .

Prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)

Prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)

Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y^2+1,yz),(xz,yz,z^2+1)|=1+x^2+y^2+z^2

|[x,1,y+z],[y,1,z+x],[z,1,x+y]|=

|[1, x, x^2 ],[1, y, y^2],[1, z, z^2]|=

The value of |(x+y,y+z,z+x),(x,y,z),(x-y,y-z,z-x)|=

Let Delta=|(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1)| and Delta_(1)=|(A,B,C),(x,y,z),(zy,zx,xy)| then