Because of abc>0, then A, B and C are not equal to 0, then A, B and c >；; 0 or

Suppose a < 0, BC < 0, A+B+C > 0, then B+C >-A > 0.

So a (b+c) < 0,

Therefore, a (b+c)+BC = AB+AC+BC < 0, which is different from AB+AC+BC >; 0 does not match,

So a > 0, similarly: b, c > 0.