若x-y=-z则(x²+y²)+(xz-yz)等于

Question

打错了（x²+y²)+(xz-yz） 是（x²-y²）

Answer 1

(x²-y²)+(xz-yz)
=(x-y)(x+y)+(x-y)z
=-zx-zy+zx-yz
=-2yz追问

为什么提取x-y 不提取z啊

追答

一样的，
但一般是提取x-y
因为能看出x-y是公因式。

追问

那到底楼上的对不对啊

追答

不对
(x²-y²)+(xz-yz)
=(x-y)(x+y)+(x-y)z
=(x-y)(x+y+z)
因为是x-y=z,不是x+y=-z
所以
错的。
除非x+y=-z

本回答被提问者采纳

Answer 2

(x²+y²)+(xz-yz)=(x-y)^2+2xy+(x-y)*z=z^2+2xy-z^2=2xy

(x-y)^2为（x+y）的平方

Answer 3

没补充前是2xy,补充后是-2yz

Answer 4

(x²+y²)+(xz-yz)
=(x²+y²)+z(x-y)
=x²+y²-(x-y)(x-y)
=x²+y²-x²+2xy-y²
=2xy

(x²-y²)+(xz-yz)
=(x-y)(x+y))+z(x-y)
=(x-y)(x+y+z)
=(x-y)(-z+z)
=(x-y)*0
=0

Answer 5

-2yz