因式分解：（x+y)³+2xy-2x²y-2xy²-1

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因式分解：（x+y)³+2xy-2x²y-2xy²-1
因式分解：（x+y)³+2xy-2x²y-2xy²-1

因式分解：（x+y)³+2xy-2x²y-2xy²-1
（x+y)³+2xy-2x²y-2xy²-1
=(x+y)³-1 -2xy(x+y-1)
=(x+y-1)[(x+y)²+(x+y)+1]-2xy(x+y-1)
=(x+y-1)[(x+y)²+(x+y)+1-2xy]
=(x+y-1)(x²+y²+x+y+1)