" 53."|[1,a,a^(2)],[1,b,b^(2)],[1,c,c^(2)]|=|[1,bc,b+c],[1,ca,c+a],[1,ab,a+b]|

Without expanding show that : |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=|(1,bc,b+c),(1,ca,c+a),(1,ab,a+b)|

|[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b)]|=0

If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,ab, c]| , then

Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

|[a,a^(2),bc],[b,b^(2),ca],[c,c^(2),ab]|=|[1,a^(2),a^(3)],[1,b^(2),b^(3)],[1,c^(2),c^(3)]|

Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

Without expanding the determinant, Prove that |[a,a^2, bc],[b,b^2,ca],[c,c^2,ab]|= |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|

Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]| = |[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|