Show that `|[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]|=abc(a-b)(b-c)(c-a)`

Prove that |[a,b,c] , [a^2,b^2,c^2] , [a^3,b^3,c^3]|= abc(a-b)(b-c)(c-a)

Show that det[[1,1,1a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)det[[a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)det[[a^(2),b^(2),c^(2)a^(3),b^(3),c^(3)]]=(b-c)(c-a)(a-b)(bc+ca+ab)

The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| is (A) (a+b+c),(a^2+b^2+c^2) (B) a^3+b^3+c^3-3abc (C) (a-b)(b-c)(c-a) (D) 0

Show that |[b+c,c+a,a+b] , [a+b,b+c,c+a] , [a,b,c]|=a^3+b^3+c^3-3abc

If A=|(1,1,1),(a,b,c),(a^3,b^3,c^3)|, B=|(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3)|, C=|(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)| , then which relation is correct :

Show that: ,3a,-a+b,-a+c-b+a,3b,-b+c-c+a,-c+b,3c]|=3(a+b+c)(ab+bc+ca)

Show that |[a_(1),b_(1),-c_(1)],[-a_(2),-b_(2),c_(2)],[a_(3),b_(3),-c_(3)]|=|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(3)]|

Show that ,,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]|=2(a+b+c)^(3)

Show that ,,a+b+2c,a,bc,b+c+2a,bc,a,c+a+2b]|=2(a+b+c)^(3)

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a)(a+b+c)