" 43.Without expanding prove that,"|[b^(2)c^(2),bc,b+c],[c^(2)a^(2),ca,c+a],[a^(2)b^(2),ab,a+b]|=0

Without expanding prove that, |{:(b^2c^2,bc,b+c),(c^2a^2,ca,c+a),(a^2b^2,ab,a+b):}|=0

|[b^2c^2,bc,b+c] , [c^2a^2,ca,c+a] , [a^2b^2,ab,a+b]|=0

Prove that [[b^2c^2, bc,b+c],[c^2a^2,ca,c+a],[a^2b^2,ab,a+b]] = 0

If a,b and c are non- zero real number then prove that |{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0

If a,b and c are non- zero real number then prove that |{:(b^(2)c^(2),,bc,,b+c),(c^(2)a^(2),,ca,,c+a),(a^(2)b^(2),,ab,,a+b):}| =0

Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=0

Without expanding prove that: |[1,a,a^(2)-bc],[1,b,b^(2)-ca],[1,c,c^(2)-ab]|=0

Without expanding prove that |{:(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab):}|=0

Show that |(b+c,bc,b^(2)c^(2)),(c+a,ca,c^(2)a^(2)),(a+b,ab,a^(2)b^(2))|=0 .

Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+b|=0 .