By using properties of determinants. Show that:`|xx^2y z y y^2z x z z^2x y|=(x-y)(y-z)(z-x)(x y+y z+z x)`

Using the properties of determinants, show that: abs((x,x^2,yz),(y,y^2,xz),(z,z^2,xy))=(x−y)(y−z)(z−x)(xy+yz+zx)

Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

Prove the following using properties of determinants det[[x,y,zx^(2),y^(2),z^(2)y+z,z+x,x+y]]=(x-y)(y-z)(z-x)(x+y+z)]|=

Using properties of determinant prove that: |[1,x+y, x^2+y^2],[1, y+z, y^2+z^2],[1, z+x, z^2+x^2]|= (x-y)(y-z)(z-x)

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

Using properties of determinants, prove that |[a+x,y,z],[x,a+y,z],[x,y,a+z]|=a^2(a+x+y+z)

Using properties of determinants, prove that |[2y,y-z-x,2y],[2z,2z, z-x-y],[ x-y-z, 2x,2x]|=(x+y+z)^3

Use properties of determinants to evaluate : |{:(x+y,y+z,z+x),(z,x,y),(1,1,1):}|

Prove the following : |{:(x,x^(2),y+z),(y,y^(2),z+x),(z,z^(2),x+y):}|=(y-z)(z-x)(x-y)(x+y+z)

Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(x-y)(y-z)(z-x)(x+y+z)(x^2+y^2+z^2)dot