x的3次方减去的y的3次方如何分解因式
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x^3-y^3
=x^3-x^2y+x^2y-y^3
=(x^3-x^2y)+(x^2y-y^3)
=x^2(x-y)+(x^2-y^2)y
=x^2(x-y)+(x-y)y(x+y)
=x^2(x-y)+(x-y)(xy+y^2)
=(x-y)(x^2+xy+y^2)
=x^3-x^2y+x^2y-y^3
=(x^3-x^2y)+(x^2y-y^3)
=x^2(x-y)+(x^2-y^2)y
=x^2(x-y)+(x-y)y(x+y)
=x^2(x-y)+(x-y)(xy+y^2)
=(x-y)(x^2+xy+y^2)
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