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a(x-y)(x+y)-b(y-x)(x+y)-c(x-y)^2(y+x)提取公因式

分类: 作业答案 • 2022-06-13 11:47:00
问题描述：

a(x-y)(x+y)-b(y-x)(x+y)-c(x-y)^2(y+x)提取公因式

答

a(x-y)(x+y)-b(y-x)(x+y)-c(x-y)^2(y+x)
a(x-y)(x+y)+b(x-y)(x+y)-c(x-y)(x-y)(x+y)
(x-y)(x+y)(a+b-c(x-y))

答

原式=(x^2-y^2)a-(x^2-y^2)b-(x^2-y^2)(x-y)c
=(x^2-y^2)(a-b-cx-cy)
=(x+y)(x-y)(a-b-cx-cy)

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