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

Show that |(1,1,1), (a,b,c),(a^2,b^2,c^2)|=(a-b)(b-c)(c-a)

1,1,1a,b,ca^(2),b^(2),c^(2)]|=(a-b)(b-c)(c-a)

([1,1,1a,b,ca^(2),b^(2),c^(2)])=(a-b)(b-c)(c-a)

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

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

det[[ Prove that ,a,b^(2),ca^(2),b^(2),c^(2)a+c,c+a,a+b]]=(a-b)(b-c)(c-a)(a+b+c)

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

Prove that |[(b+c)^2, a^2, bc],[(c+a)^2, b^2, ca],[(a+b)^2, c^2, ab]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

Prove that Delta = |{:(1,,1,,1),(a,,b,,c),(bc+1^(2),,ac+b^(2),,ab+c^(2)):}| = 2(a-b)(b-c)(c-1)

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