因式分解:(x^2)y-(y^2)z+(z^2)x-(x^2)z+(y^2)x+(z^2)y-2xyz

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因式分解:(x^2)y-(y^2)z+(z^2)x-(x^2)z+(y^2)x+(z^2)y-2xyz因式分解:(x^2)y-(y^2)z+(z^2)x-(x^2)z+(y^2)x+(z^2)y-2x

因式分解:(x^2)y-(y^2)z+(z^2)x-(x^2)z+(y^2)x+(z^2)y-2xyz
因式分解:(x^2)y-(y^2)z+(z^2)x-(x^2)z+(y^2)x+(z^2)y-2xyz

因式分解:(x^2)y-(y^2)z+(z^2)x-(x^2)z+(y^2)x+(z^2)y-2xyz
x²y -y²z +z²x -x²z +y²x +z²y -2xyz
=(y-z)x² -(y-z)yz +(z²+y²)x -2xyz
=(y-z)(x²-yz) +(y-z)²x
=(y-z)(x²-yz +yx -zx)
=(y-z)[x(x-z)-y(z-x)]
=(y-z)(x+y)(x-z)
这题目其实关键是一个“凑”字
根据数学的对称性,抓对“凑”起来就行了!
要说技巧就是经验啦!
要是一时没经验,就一对一对抓,反正也就10来种凑对的方法,不多

原式=(y-z)x^2+(z^2+y^2-2yz)x+zy(z-y)
=[(y-z)x+y^2-yz][x-z]
=(y^2+(x-z)y-zx)(x-z)
=(y+x)(y-z)(x-z)
本题用了主元

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