Assuming that det(AB) = det(A)det(B) for 3x3 matricies, prove that...

| a+b+c , a^2+b^2+c^2 , a^3+b^3+c^3|

|a^2+b^2+c^2 , a^3+b^3+c^3 , a^4+b^4+c^4| = abc(b-c)^2(c-a)^2(a-b)^2

|a^3+b^3+c^3 , a^4+b^4+c^4 , a^5+b^5+c^5|

The problem I encounter with this problem is that I either find that I get an answer of 0 or I end up with a very large equation which I can't find a way to cancel. Any help would be apreciated.

Rodregez