Question

已知x^2-y^2-z^2=0 分解因式x^3-y^3-z^3

（x^2表示x的二次方）
要到一次乘积.
请各位高手一定要给出过程呀，不胜感激！！！

Answer 1

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

Answer 2

(x-z)(x-y)(2x y z) 首先由给定的式子消y^3得一个式子.可以由此提出x-z.在剩余部分消z^2最后以x为主元十字相乘可得答案.请原谅我的简略.我用的手机

Answer 3

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

Answer 4

(x-y)(x^2+x*y+y^2-x*z-y*z)