kill(all);

van=facebook.com/LearningCalculus;

p1(a,b,c):=(a+b)*(b+c)*(c+a) + a*b*c;

factor(p1);

p1(x,y,z);

p2(a,b,c):=(a-b)^3+(b-c)^3+(c-a)^3;

p2(x,y,z);

p3(a,b,c):=(a^4+b^4+c^4-2*a^2*b^2-2*b^2*c^2-2*c^2*a^2);

factor(p3(x,y,z));

p4(a,b,c):=((a-b)^5+(b-c)^5+(c-a)^5);

factor(p4(x,y,z));

factor(%);

fullratsimp(%);