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

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

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)

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

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

S.T |(1,a,a^2),(1,b,b^2),(1,c,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) .

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

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

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

Without expanding show that : |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=|(1,bc,b+c),(1,ca,c+a),(1,ab,a+b)|