Prove that ` |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,c,,c),(x,,y,,z),(yz,,xz,,xy):}|`

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,b,,c),(x,,y,,z),(yz,,xz,,xy):}|

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,b,,c),(x,,y,,z),(yz,,xz,,xy):}|

Without expanding the determinant , prove that |{:(ax,by,cz),(x^2,y^2,z^2),(1,1,1):}|=|{:(a,b,c),(x,y,z),(yz,zx,xy):}|

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 |{:(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: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]| = |[a,b,c],[x,y,z],[yz,zx,yx]|

Let Delta_(1)=|{:(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1):}| and Delta_(2)=|{:(A,B,C),(x,y,z),(yz,zx,xy):}| , then :

If Delta_(1)=|{:(Ax,x^(2),1),(By,y^(2),1),(Cz,z^(2),1):}|" and "Delta_(2)=|{:(A,B,C),(x,y,z),(yz,zx,xy):}| , then