Determinant form of `(x-y)(y-z)(z-x)`

Determinant , form (x-y)(y-z)(z-x)(xy+yz+zx), of

Determinant (x-y)(y-z)(z-x)(x+y+z)

The simplified form of x(y-z)(y+z)+y(z-x)(z+x)+z(x-y)(x+y) is

Area of the triangle formed by (x,y+z),(y,z+x),(z,x+y) is

By using properties of determinant prove that |(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0

Find the value of the determinant |"cos"(x-y)"cos"(y-z)"cos"(z-x)"cos"(x+y)"cos"(y+z)cos(z+x)"sin"(x+y)"sin"(y+z)s in(z+x)|

The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,y,z)| , is

What is the determinant of the matrix ({:(x,y,y+z),(z,x,z+x),(y,z,x+y):}) ?

The repeated factor of the determinant |(y +z,x,y),(z +x,z,x),(x +y,y,z)| , is

Using properties of determinants, prove that |{:(x,y,z),(x^(2),y^(2),z^(2)),(y+z,z+x,x+y):}|=(x-y)(y-z)(z-x)(x+y+z)