分解因式：x^2y+xy^2-x^2-y^2-3xy+2x+2y-1
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x^2y+xy^2-x^2-y^2-3xy+2x+2y-1
=(x^2y+xy^2)-(x^2+y^2+2xy)-(xy-x-y+1)+(x+y)
=xy(x+y)-(x+y)^2-(x-1)(y-1)+(x+y)
=(x+y)(xy-x-y+1)-(x-1)(y-1)
=(x+y)(x-1)(y-1)-(x-1)(y-1)
=(x-1)(y-1)(x+y-1)
=(x^2y+xy^2)-(x^2+y^2+2xy)-(xy-x-y+1)+(x+y)
=xy(x+y)-(x+y)^2-(x-1)(y-1)+(x+y)
=(x+y)(xy-x-y+1)-(x-1)(y-1)
=(x+y)(x-1)(y-1)-(x-1)(y-1)
=(x-1)(y-1)(x+y-1)
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