Show without expanding at any stage that: ` [(a-1)^2, a^2+1, a],[(b-1)^2, b^2+1,b],[(c-1)^2, c^2+1, c]|=0 `

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, a,bc],[1/b,b,ca],[1/c, c, ab]|=0

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

Show without expanding at any stage that: det [ [a,b,c],[a+2x,b+2y,c+2z],[x,y,z]] =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 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: [a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]|=2|[a,b,c],[b,c,a],[c,a,b]|

Show without expanding that |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=|[1,b c, b+c],[1,c a, c+a],[1,a b, a+b]|