Without expanding the determinant, prove that `|a a^2b c bb^2c a cc^2a b|=|1a^2a^3 1b^2b^3 1c^2c^3|`

Prove that: |1a a^2-b c1bb^2-c a1cc^2-a b|=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 ,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)]]

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: [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 prove that: |[1,a,a^(2)-bc],[1,b,b^(2)-ca],[1,c,c^(2)-ab]|=0

Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)| .

without expanding evaluate the determinant Delta=det[[1,1,1a,b,ca^(2),b^(2),c^(2)]]

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)