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

Prove that det[[1,a,a^(2)-bc1,b,b^(2)-ca1,c,c^(2)-ab]]=0

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

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

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])

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

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]|

Without expanding the determinant,prove ,a,a^(2),bcb,b^(2),cac,c^(2),ab]|=det[[1,a^(2),a^(3)1,b^(2),b^(3)1,c^(2),c^(3)]]

Using the property of determinants and without expanding,prove that: det[[1,bc,a(b+c)1,ca,b(c+a)1,ab,x(a+b)]]=0

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

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