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几道因式分解的小题1 (z-x)^3-(y+z)^32 X^3-3x+23 ab^2-ac^2+4ac-4a4 (x-y

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几道因式分解的小题
1 (z-x)^3-(y+z)^3
2 X^3-3x+2
3 ab^2-ac^2+4ac-4a
4 (x-y)^2+12(y-x)z+36z^2
1 (z-x)^3-(y+z)^3
=(z-x-y-z)( (z-x)^2+(z-x)(y+z)+(y+z)^2)
=(-x-y)( (z-x)^2+(z-x)(y+z)+(y+z)^2) 感觉到这一步就可以了
=-(x+y)(x^2+2y^2+2z^2+2yz-3xz-xy)
2 X^3-3x+2
=X^3-1-3X+3
= ( X^3-1)-3 (X-1)
= (X-1)(X^2+X+1-3)
= (X-1)(X^2+X-2)
3 ab^2-ac^2+4ac-4a
=a(b^2-c^2+4c-4)
= a[b^2-(c-2)^2]
=a(b+c-2)(b-c+2)
4 (x-y)^2+12(y-x)z+36z^2
=(x-y)^2-12(x-y)z+36z^2
=[x-y-6z]^2