Show without expanding at any stage 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]| `

Show without expanding at any stage that: [1/a, a,bc],[1/b,b,ca],[1/c, c, 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)]|

Show without expanding at any stage that: [1/a, a^2, bc],[1/b, b^2, ca],[1/c, c^2, ab]|=0

Show without expanding at any stage that: [1,a,b+c],[1,b,c+a],[1,c,a+b]|=0

Show without expanding at any stage that: [1,a,bc],[1,b,ca],[1,c,ab]|=|[1,a,a^2],[1,b,b^2],[1,c,c^2 ]|

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

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

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

Show without expanding at any stage that: | [1,bc, a(b+c)],[1,ca, b(c+a)],[1,ab, c(a+b)]|=0

Show without expanding at stage that : det[[1,ca,b(c+a)1,ab,c(a+b)]]=0