分解因式x²y²+xy-x²-y²+x+y+2

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分解因式x²y²+xy-x²-y²+x+y+2分解因式x²y²+xy-x²-y²+x+y+2分解因式x²y&#

分解因式x²y²+xy-x²-y²+x+y+2
分解因式x²y²+xy-x²-y²+x+y+2

分解因式x²y²+xy-x²-y²+x+y+2
x²y²+xy-x²-y²+x+y+2
=（x²y²-x²-y²+1）+（xy+x+y+1）
=（x²-1）（y²-1）+（x+1)(y+1)
=（x+1）（x-1）(y+1)(y-1）+（x+1)(y+1)
=（x+1)(y+1)[(x-1)(y-1)+1]
=（x+1)(y+1)(xy-x-y+2)