" Show that "|[bc,b+c,1],[ca,c+a,1],[ab,a+b,1]|=(a-b)(b-c)(c-a)

|[1, 1, 1], [a, b, c], [bc, ca, ab]| = (a-b)(b-c)(c-a)

|[1,1,1],[a,b,c],[bc,ca,ab]|=(a-b)(b-c)(c-a)

det[[bc,b+c,1ca,c+a,1ab,a+b,1]]=

Prove that: {:|(bc,a,1),(ca,b,1),(ab,c,1)| = (a-b)(b-c)(a-c)

|[1,a, bc] ,[1, b, ca], [1, c, ab]| = (a-b)(b-c)(c-a)

Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .

Using properties of determinant show that: det[[1,a,-bc1,b,-ca1,c,-ab]]=(a-b)(b-c)(c-a)det[[1,b,-ca1,c,-ab]]=(a-b)(b-c)(c-a)

Using properties of determinants , prove that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)