(x+y+z)(x-y+z)+(y-x+z)(y-x-z)求过程

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(x+y+z)(x-y+z)+(y-x+z)(y-x-z)求过程
(x+y+z)(x-y+z)+(y-x+z)(y-x-z)求过程

(x+y+z)(x-y+z)+(y-x+z)(y-x-z)求过程
(x+y+z)(x-y+z)+(y-x+z)(y-x-z)
=(x+y+z)(x-y+z)-(y-x+z)(x-y+z)
=((x+y+z)-(y-x+z))(x-y+z)
=(2x)(x-y+z)
=2x(x-y+z)
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先看题,分解成两部分,以 + 号为界,可见只要把 + 号左边第二个公因式提出“- ”号,就可以合并了。
(x+y+z)(x-y+z)+(y-x+z)(y-x-z)
= -(x+y+z)(y-x-z)+(y-x+z)(y-x-z)
=(y-x-z)(y-x+z-x-y-z)
=2x(x+z-y)

(x+y+z)(x-y+z)+(y-x+z)(y-x-z)
=(x+y+z)(x-y+z)-(y-x+z)(x+z-y)
=(x-y+z)[(x+y+z)-(y-x+z)]
=(x-y+z)(x+y+z-y+x-z)
=(x-y+z)2x
=2x(x-y+z)