If `Delta_1 = |[1,1,1] , [x^2, y^2, z^2] , [x,y,z]|` and `Delta_2=|[1,1,1] , [yz, zx, xy] , [x,y,z]|` then without expanding show that `Delta_1= Delta_2`

If D_1=|[1, 1, 1],[x^2,y^2,z^2],[x, y, z]| and D_2=|[1, 1, 1],[yz, zx,xy], [x, y, z]| without expanding prove that D_1=D_2

If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expanding or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

If Delta_1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta_2=|[q,-b, y],[-p, a,-x],[ r,-c, z]|, without expending or evaluating Delta_1 and Delta_2 , show that Delta_1+Delta_2=0

If Delta_(1)=|[a,b, c],[x, y, z],[p,q ,r]|"and "Delta_(2) |[q,-b, y],[-p, a, -x],[r,-c ,z]| then without expanding Delta_(1) " and "Delta_(2), "prove that "Delta_(1) + Delta_(2) =0

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]|

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

Delta= |[Ax,x^(2),1],[By,y^(2),1],[Cz, z^(2),1]| and Delta_(1)= |[A,B,C],[x,y,z],[zy, zx,xy]|

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

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 .