[|[1,y,y^(2)],[1,z,z^(2)]|=?],[[" (a) "0," (b) "(x-],[" (c) "(y-x)(y-z)(z-x)," (d) nor "]]

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

|[yz,x,x^(2)],[zx,y,y^(2)],[xy,z,z^(2)]|=|[1,x^(2),x^(3)],[1,y^(2),y^(3)],[1,z^(2),z^(3)]|

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

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

If "Delta"=|(1,x,x^2),( 1,y, y^2),( 1,z, z^2)| , "Delta"_1=|(1, 1, 1),(yz, z x,x y), (x, y, z)| , then prove that "Delta"+"Delta"_1=0 .

If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}| , Delta_(1)=|{:(1,1,1),(yz,zx,xy),(x,y,z):}| , then prove that Delta+Delta_(1)=0

If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}| and Delta_(1)=|{:(1,1,1),(yz,zx,xy),(x,y,z):}| then prove that Delta+Delta_(1)=0

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)