x^3-8y^3-x^-x^2-2xy-4y^2

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x^3-8y^3-x^-x^2-2xy-4y^2

x^3-8y^3-x^-x^2-2xy-4y^2
x^3-8y^3-x^-x^2-2xy-4y^2

x^3-8y^3-x^-x^2-2xy-4y^2
题目应该是x³ -8y³ -x²-2xy-4y²吧?
x³ -8y³ -x^2-2xy-4y²
=(x³ -8y³ )-(x²+2xy+4y²)
=(x-2y)(x²+2xy+4y²)-(x²+2xy+4y²)
=(x²+2xy+4y²)(x-2y-1)
第二步利用了公式a³ -b³ =(a-b)(a²+ab+b²).式中 8y³ =(2y)³

x^3-8y^3-x^-x^2-2xy-4y^2
=(x-2y)(x²+2xy+4y²)-(x²+2xy+4y²)
=(x²+2xy+4y²)(x-2y-1)