因式分解一题,(x-2)^3-(y-2)^3-(x-y)^3
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/28 09:12:34
因式分解一题,
(x-2)^3-(y-2)^3-(x-y)^3
(x-2)^3-(y-2)^3-(x-y)^3
![因式分解一题,(x-2)^3-(y-2)^3-(x-y)^3](/uploads/image/z/18583738-34-8.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%E4%B8%80%E9%A2%98%2C%28x-2%29%5E3-%28y-2%29%5E3-%28x-y%29%5E3)
(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)^3
=(x-y)[(x-2)^2+(x-2)(y-2)+(y-2)^2-(x-y)^2]
=(x-y)(3xy-6x-6y+12) (中括号内展开,合并同类项可得)
=(x-y)[3x(y-2)-6(y-2)]
=(x-y)(y-2)(3x-6)
=3(x-y)(y-2)(x-2)
=[(x-2)-(y-2)][(x-2)^2+(x-2)(y-2)+(y-2)^2]-(x-y)^3
=(x-y)[(x-2)^2+(x-2)(y-2)+(y-2)^2-(x-y)^2]
=(x-y)(3xy-6x-6y+12) (中括号内展开,合并同类项可得)
=(x-y)[3x(y-2)-6(y-2)]
=(x-y)(y-2)(3x-6)
=3(x-y)(y-2)(x-2)