✨ ベストアンサー ✨
x³-x-y³+y+x²y-xy²
看到x³ y³ x²y xy²
而且正負號交錯
於是湊湊看(x-y)³的展開
(x³-3x²y+3xy²-y³)+4x²y-4xy²-x+y
=(x-y)³+4xy(x-y)-(x-y)
=(x-y)[(x-y)²+4xy-1]
=(x-y)[(x+y)²-1]
=(x-y)(x+y+1)(x+y-1)
✨ ベストアンサー ✨
x³-x-y³+y+x²y-xy²
看到x³ y³ x²y xy²
而且正負號交錯
於是湊湊看(x-y)³的展開
(x³-3x²y+3xy²-y³)+4x²y-4xy²-x+y
=(x-y)³+4xy(x-y)-(x-y)
=(x-y)[(x-y)²+4xy-1]
=(x-y)[(x+y)²-1]
=(x-y)(x+y+1)(x+y-1)
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