[" Prove that: "],[|[1,1,1],[a,b,c],[a^(3),b^(3),c^(3)]|=(a-b)(b-c)(c-a)(a+b+c)]

1,1,1a,b,ca^(3),b^(3),c^(3)]|=(a-b)(b-c)(c-a)(a+b+c)

Using the property of determinants and without expanding prove that abs([1,1,1],[a,b,c],[a^3,b^3,c^3])=(a-b)(b-c)(c-a)(a+b+c)

By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^3,b^3,c^3]| = (a-b)(b-c)(c-a)(a+b+c)

Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b-c)(c-a)(a+b+c)

Using properties of determinants prove the following. abs[[1,1,1],[a,b,c],[a^3,b^3,c^3]]=(a-b)(b-c)(c-a)(a+b+c)

Prove the following: [[1,1,1],[a,b,c],[a^3,b^3,c^3]] =(b-c)(c-a)(a-b)(a+b+c)

By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a) (ii) |[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Using properties of determinants, prove that |(1,a,a^(3)),(1,b,b^(3)),(1,c,c^(3))| = (a-b)(b-c)(c-a)(a+b+c) .

Prove that |[1 , a , a^3],[ 1, b, b^3],[ 1, c, c^3]|=(a-b)(b-c)(c-a)(a+b+c)

If a,b,are distinct,show that [[1,1,1a,b,ca^(3),b^(3),c^(3)]]=(b-c)*(c-a)*(a-b)(a+b+c)