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

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)

好复杂哦！

(a+b+c)^4 - (b+c)^4 - (c+a)^4 - (a+b)^4 + a^4 + b^4 + c^4
不管怎么样，都先别急于展开括号了

= (a+b+c)^4 + [ a^4 - (b+c)^4 ] + [ b^4 - (c+a)^4 ] + [ c^4 - (a+b)^4 ]
像这样分组处理，就能通过平方差，得到 (a+b+c) 就能提取公因式了

= (a + b + c)^4 + [ a" + (b + c)" ][ a" - (b + c)" ] + [ b" + (a + c)" ][ b" - (a + c)" ]
+ [ c" + (a + b)" ][ c" - ( a + b )" ]
平方差用了一次，还能再用一次

= (a +b +c)^4 + [ a" +(b+c)" ](a + b + c)[ a - (b + c) ] + [ b" +(c+a)" ](b + c + a)[ b - (a + c) ]
+ [ c" +(a+b)" ](c+a+b)[ c - (a + b) ]
除了(a+b+c) 提取公因式，还有 a -(b+c) 这几个也变化处理看看

= { (a + b + c)"' + (a" +b" +c" +2bc)[ 2a - (a + b + c) ] + (a" +b" +c" +2ac)[ 2b -