因式分解（x+y)(x+y+2xy)+(xy+1)(xy-1)

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因式分解（x+y)(x+y+2xy)+(xy+1)(xy-1)因式分解（x+y)(x+y+2xy)+(xy+1)(xy-1)因式分解（x+y)(x+y+2xy)+(xy+1)(xy-1)令x＋y＝a,

因式分解（x+y)(x+y+2xy)+(xy+1)(xy-1)
因式分解（x+y)(x+y+2xy)+(xy+1)(xy-1)

因式分解（x+y)(x+y+2xy)+(xy+1)(xy-1)
令x＋y＝a,xy＝b,则
原式＝a(a＋2b)＋(b＋1)(b－1)
＝a^2＋2ab＋b^2－1
＝(a＋b)^2－1
＝(a＋b＋1)(a＋b－1)
故原式＝(x＋y＋xy＋1)(x＋y＋xy－1)
＝(x＋1)(y＋1)(x＋y＋xy－1)

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