分解因式(x+y)(x+y+2xy)+(xy+1)(xy-1)

发布时间：2021-02-20 02:47:40

分解因式(x+y)(x+y+2xy)+(xy+1)(xy-1)

网友回答

(x+y)(x+y+2xy)+(xy+1)(xy-1)
=(x+y)^2+2xy(x+y)+(xy+1)(xy-1)
=(x+y+xy+1)(x+y+xy-1) (十字相乘法分解)
=[(x+xy)+(y+1)](x+y+xy-1)
=[x(y+1)+(y+1)](x+y+xy-1)
=(x+1)(y+1)(x+y+xy-1).
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