因式分解(x+y)^3+2xy-2x^2y-2xy^2-1

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因式分解(x+y)^3+2xy-2x^2y-2xy^2-1
因式分解(x+y)^3+2xy-2x^2y-2xy^2-1

因式分解(x+y)^3+2xy-2x^2y-2xy^2-1
(x+y)^3+2xy-2x^2y-2xy^2-1
=(x+y)^3-1+2xy-2xy(x+y)+2xy-1
=(x+y-1)[(x+y)²+(x+y)+1]-2xy(x+y-1)
=(x+y-1)(x²+2xy+y²+x+y+1-2xy)
=(x+y-1)(x²+y²+x+y+1)

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