kill(all)$

van=facebook.com/LearningCalculus$

M:matrix([b+c,a,a],[b,c+a,b],[c,c,a+b]);

determinant(M);

fullratsimp(%);

N:matrix([1,a,b+c],[1,b,a+b],[1,c,b+c]);

determinant(N);

fullratsimp(%);