初二一道提取公因式的题目[x+y-4xy÷(x+y)]×[x+y+4xy÷(x-y)]化简、提取公因式 、

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初二一道提取公因式的题目[x+y-4xy÷(x+y)]×[x+y+4xy÷(x-y)]化简、提取公因式 、

初二一道提取公因式的题目[x+y-4xy÷(x+y)]×[x+y+4xy÷(x-y)]化简、提取公因式 、
初二一道提取公因式的题目
[x+y-4xy÷(x+y)]×[x+y+4xy÷(x-y)]
化简、提取公因式 、

初二一道提取公因式的题目[x+y-4xy÷(x+y)]×[x+y+4xy÷(x-y)]化简、提取公因式 、
[x+y-4xy÷(x+y)]×[x+y+4xy÷(x-y)]
=(x-y)^2/(x+y)×(x^2-y^2+4xy)/(x-y)
=(x-y)(x^2-y^2+4xy)/(x+y)

先通分得到[(x^2+y^2-4xy)*(x^2-y^2+4xy)]/[(x-y)(x+y)]然后

[(x+y)(x+y)-4xy]/(x+y)×[(x+y)(x-y)+4xy]/(x-y)
=(xx-2xy+yy)(xx-yy+4xy)/(x+y)(x-y)
=(x-y)(x-y)(xx-yy+4xy)/(x+y)(x-y)
=(x-y)(xx-yy+4xy)/(x+y)
注:我晕,平方我不知道怎么打。就用xx yy来代替。希望你看得懂。

我觉得你题抄错了,第二个中括号里应该是x-y,不是x+y吧
[x+y-4xy÷(x+y)]×[x-y+4xy÷(x-y)]
=[(x+y)^2÷(x+y)-4xy÷(x+y)]×[(x-y)^2÷(x-y)+4xy÷(x-y)]
=[(x^2+2xy+y^2-4xy)÷(x+y)]×[(x^2-2xy+y^2+4xy)÷(x-y)]
=[(x-y)^2÷(x+y)]×[(x+y)^2÷(x-y)]
=(x-y)(x+y)
=x^2-y^2