（x+y）三次方乘以（x-y）减（x+y）（x-y）三次方（x+y）三次方乘以（x-y）减（x+y）（x-y）三次方因式分解

分类: 作业答案 • 2021-12-19 15:03:09

问题描述：

（x+y）三次方乘以（x-y）减（x+y）（x-y）三次方
（x+y）三次方乘以（x-y）减（x+y）（x-y）三次方
因式分解

答

(x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)((x+y)^2-(x-y)^2)
=4(x^2-y^2)xy
=4x^3y-4xy^3

答

（x+y）^3(x-y)-(x+y)(x-y)^3=4xy(x+y)(x-y)

答

原式=（x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)[(x+y)^2-(x-y)^2]
=(x+y)(x-y)[x^2+2xy+y^2-x^2+2xy-y^2]
=4xy(x+y)(x-y)