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)`

Using properties of determinant show 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)

Using properties of determinants, prove the following : |[a, a^2,bc],[b,b^2,ca],[c,c^2,ab]|=(a-b)(b-c)(c-a)(b c+c a+a b)

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

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

Using properties of determinants, prove that |{:(,a,b,b+c),(,c,a,c+a),(,b,c,a+b):}|=(a+b+c) (a-c)^2

using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

3. Using properties of determinants, show that :|[b+c,a,b] , [c+a,c,a] , [a+b,b,c]| = (a + b + c) (a-c)^2