The value of the determinant `|{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}|` is equal to

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Find the value of the "determinant" |{:(1,x,y+z),(1,y,z+x),(1,z,x+y):}|

Given that xyz = -1 , the value of the determinant |(x,x^(2),1 +x^(3)),(y,y^(2),1 + y^(3)),(z,z^(2),1 +z^(3))| is

The value of the determinant |{:(1 , x , x+ z) , (1 , y , z + x) , (1 , z , x + y):}| is

The value of the determinant |{:(x^(2),1,y^(2)+z^(2)),(y^(2),1,z^(2)+x^(2)),(z^(2),1,x^(2)+y^(2)):}| is :

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

Without expanding the determinants, show that |(1,x,x^2),(1,y,y^2),(1,z,z^2)|=(y-x)(z-y)(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)

The value of |{:(x,x^2-yz,1),(y,y^2-zx,1),(z,z^2-xy,1):}| is