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x2y2+xy-x2-y2+x+y+2分解因式,

题目详情
x2y2+xy-x2-y2+x+y+2分解因式,
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答案和解析
原式=(x²y²-x²-y²+1)+(xy+x+y+1)=[x²(y²-1)-(y²-1)]+[x(y+1)+(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)...