Question

(a-b-c)的三次方

Answer 1

(a+b+c)^3-(b+c-a)^3-(c+a-b)^3-(a+b-c)^3
=[(a+b+c)^3-(b+c-a)^3]-[(c+a-b)^3+(a+b-c)^3]
=[(a+b+c)-(b+c-a)][(a+b+c)^2+(a+b+c)(b+c-a)+(b+c-a)^2]-[(c+a-b)+(a+b-c)][(c+a-b)^2-(c+a-b)(a+b-c)+(a+b-c)^2]
=2a[2a^2+2b^2+2c^2+4bc+(b+c)^2-a^2]-2a[2a^2+2b^2+2c^2-4bc+(b-c)^2-a^2]
=2a(3b^2+3c^2+a^2+4bc)-2a(3b^2+3c^2+a^2-4bc)
=8bc+8bc
=16bc
打字不易，如满意，望采纳。

Answer 2

解：
(a-b-c)³
=(a-b-c)²(a-b-c)
=[(a-b)²-2c(a-b)+c²](a-b-c)
=(a²-2ab+b²-2ac+2bc+c²)(a-b-c)
=a³-a²b-a²c-2a²b+2ab²+2abc+ab²-b³-b²c-2a²c+2abc+2ac²+2abc-2b²c-2bc²+ac²-c²b-c³
=a³-b³-c³-3a²b-3a²c+3ab²-3b²c+3ac²-3bc²+6abc