prove `|(x^2,y^2,z^2),((x+1)^2,(y+1)^2,(z+1)^2), ((x-1)^2,(y-1)^2,(z-1)^2)|=-4(x-y)(y-z)(z-x)`

Prove that |{:(x^2,y^2,z^2),((x+1)^2,(y+1)^2,(z+1)^2),((x-1)^2,(y-1)^2,(z-1)^2):}|=-4(x-y)(y-z)(z-x)

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

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)

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

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)

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zy,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(y-z)(z-x)(x-y)(yz+zy+xy)

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