题目

(x加y加z)3次方--x3次方-y3次方-z3次方.

提问时间：2020-07-26

答案

a^3 + b^3 = (a + b)(a^2 - ab + b^2)
a^3 - b^3 = (a - b)(a^2 + ab + b^2)

(x+y+z)^3 -x^3 - y^3 - z^3
=(y+z)[(x+y+z)^2 + (x+y+z)x +x^2] - (y+z)(y^2 - yz +z^2)
=(y+z)(3x^2 + y^2 + z^2 + 3xy + 3xz + 2yz - y^2 +yz -z^2)
=3(y+z)(x^2 + xy +xz + yz)
=3(x+y)(x+z)(y+z)