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问题: 初中因式分解

(xy)^2+2xy(x+y+2)+2(x+y)+x^2+y^2+1

解答:

(xy)^2+2xy(x+y+2)+2(x+y)+x^2+y^2+1
=(xy+1)^2+2(xy+1)(x+y)+(x+y)^2
=(xy+x+y+1)^2=(x+1)^2(y+1)^2