因式分解(a+b+c)^4-(b+c)^4-(c+a)^4-(a+b)^4+a^4+b^4+c^4

Question

因式分解(a+b+c)^4-(b+c)^4-(c+a)^4-(a+b)^4+a^4+b^4+c^4

Answer 1

原式=[a^4+4a^3(b+c)+6a^2(b+c)^2+4a(b+c)^3+(b+c)^4]- (b+c)^4-[c^4+4c^3a+6c^2a^2+4ca^3+a^4]-
[a^4+4a^3b+6a^2b^2+4ab^3+b^4]+a^4+b^4+c^4
=12a^2bc+12ab^2c+12abc^2
=12abc(a+b+c)