`|(1+x,y,z),(x,1+y,z),(x,y,1+z)|=1+x+y+z`

Find the value of : |(1+x,y,z),(x,1+y,z),(x,y,1+z)|

|(x,1,y+z),(y,1,z+x),(z,1,x+y)|=

A(x, y, z)=" min. "(x+y, y+z, z+x) B(x, y, z)="max "(x-y, y-z, z-x) C(x, y, z)=" max"(A(x, y, z), B(x, y, z)) D(x, y, z)=" min "(A(x, y, z), B(x, y, z)) Whgat is the value D(1, 2, C(0, 1, 2)) ?

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

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)

Prove that : |{:(1,1,1),(x,y,z),(x^(3),y^(3),z^(3)):}|=(x-y)(y-z)(x+y+z)

Prove that |(1,x,x^2),(1,y,y^2),(1,z,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 |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y) .