सिद्ध कीजिये `|(1,x,x^2),(1,y,y^2),(1,z,z^2)|`= (x-y)(y-z)(z-x)

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)|=(x-y)(y-z)(z-x)

Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

using the properties of determinants 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)

Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

Solve that |(y+z,x,x^(2)),(z+x,y,y^(2)),(x+y,z,z^(2))|=(x+y+z)(x-y)(y-z)(z-x)

Show that |(1,1,1),(x,y,z),(x^(2),y^(2),z^(2))|=(x-y)(y-z)(z-x)

Prove that : =|{:(1,1,1),(x,y,z),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

Prove that : =2|{:(1,1,1),(x,y,rz),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

Using the properties of determinant, show 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)

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)