分解因式(x+y)(x+y+2xy)+x^2y^2-1

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

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

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

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

(x+y)(x+y+2xy)+(x^2)(y^2)-1
=(x+y)[(x+y)+2xy]+(xy)^2-1
=(x+y)^2+2(x+y)(xy)+(xy)^2-1
=[(x+y)+xy]^2-1
=(x+y+xy+1)(x+y+xy-1)

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