a加b加c的3次方减a的三次方减b的三次方减c的三次方怎么因式分解

(a+b+c)³-a³-b³-c³ =(a+b+c-a)[(a+b+c)²+a(a+b+c)+a²]-(b+c)(b²-bc+c²) =(b+c)(a²+b²+c²+2ab+2ac+2bc+a²+ab+ac+a²)-(b+c)(b²-bc+c²) =(b+c)(3a²+3ab+3ac+3bc) =3(b+c)[a(a+b)+c(a+b)] =3(a+b)(a+c)(b+c)

(a + 2b + c)^3 - (a + b)^3 - (b + c)^3 = (a + 2b + c)^3 - [(a + b)^3 + (b + c)^3] =(a +2b+ c)^3-[(a+ b)+(b + c)][(a+b)^2+(b+c)^2-(a+b)(b + c)] = (a + 2b + c)[3 b^2 + 3ab + 3ac + 3bc) = 3 (a + b) (b + c) (a + 2 b + c)