x^3+3xy+y^3-1因式分解

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x^3+3xy+y^3-1因式分解x^3+3xy+y^3-1因式分解x^3+3xy+y^3-1因式分解x³+3xy+y³-1=x³+3x²y+3xy²

x^3+3xy+y^3-1因式分解
x^3+3xy+y^3-1因式分解

x^3+3xy+y^3-1因式分解
x³+3xy+y³-1
=x³+3x²y+3xy²+y³-3x²y-3xy²+3xy-1
=(x+y)³-1+3xy(1-x-y)
=(x+y-1)[(x+y)²+(x+y)+1]+3xy(1-x-y)
=(x+y-1)(x²-xy+y²+x+y+1)