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

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

Using properties of determinants, prove that |[a,b,c] , [a^2,b^2,c^2] , [b+c,c+a,a+b]|=(a+b+c)(a-b)(b-c)(c-a)

Prove that |b+c a-b a c+a b-c b a+b c-a c|=3a b-a^3-b^3-c^3dot

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

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

Prove that |[a+b+c, -c, -b],[-c, a+b+c, -a],[-b, -a, a+b+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)

Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a+b+c|=2(a+b)(b+c)(c+a)

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