Show that `|{:(bc,b-c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)`

|(b+c,a,1),(c+a,b,1),(a+b,c,1)|=

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

Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(ab+bc+ca)

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

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

Without expanding the determinant, prove that |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|

Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

Match the following from List - I to List - II {:("List-I","List-II"),((I)|{:(1,1,1),(a,b,c),(bc,ca,ab):}|=,(a)(a-b)(b-c)(c-a)),((II)|{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(3),b^(3),c^(3)):}|=,(b)(a-b)(b-c)(c-a)abc),((III)|{:(1,1,1),(a,b,c),(a^(3),b^(3),c^(3)):}|=,(c)(a-b)(b-c)(c-a)(a+b+c)):}

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