(x-2)^3-(y-2)^3-(x-y)^3 (2x^2-3x+1)^2-22x^2+33x-1 ab(a+b)_^2-(a+b)^2+1分解因式

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(x-2)^3-(y-2)^3-(x-y)^3 (2x^2-3x+1)^2-22x^2+33x-1 ab(a+b)_^2-(a+b)^2+1分解因式
(x-2)^3-(y-2)^3-(x-y)^3 (2x^2-3x+1)^2-22x^2+33x-1 ab(a+b)_^2-(a+b)^2+1
分解因式

(x-2)^3-(y-2)^3-(x-y)^3 (2x^2-3x+1)^2-22x^2+33x-1 ab(a+b)_^2-(a+b)^2+1分解因式
(x-2)^3-(y-2)^3-(x-y)^3
=[(x-2)-(y-2)][(x-2)^2+(x-2)(y-2)+(y-2)^2]-(x-y)(x^2+xy+y^2)
=(x-y)(x^2-4x+4+xy-2x-2y+4+y^2-4y+4)-(x-y)(x^2+xy+y^2)
=(x-y)(x^2-4x+4+xy-2x-2y+4+y^2-4y+4-x^2-xy-y^2)
=(x-y)(-6x-6y+12)
=-6(x-y)(x+y-2)
(2x^2-3x+1)^2-22x^2+33x-1
=(2x^2-3x+1)^2-11（2x^2-3x+1）+10
把2x^2-3x+1看成一个数,十字法分解因式
=(2x^2-3x+1-10)(2x^2-3x+1-1)
＝（2x^2-3x-9）（2x^2-3x）
＝（2x+3)(x-3)（2x^2-3x）
=x（2x+3)(x-3)(2x-3)
ab（a+b）^2-(a+b)^2+1
十字相乘法
=a(a+b)b(a+b)-(a+b)(a+b)+1
=a(a+b)b(a+b)-a(a+b)-b(a+b)+1
=a(a+b)[b(a+b)-1]-b(a+b)+1
=a(a+b)[b(a+b)-1]-[b(a+b)-1]
=[a(a+b)-1][b(a+b)-1]

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