因式分解:x^3 -3x^2 y + 3xy^2 - y^3
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因式分解:x^3 -3x^2 y + 3xy^2 - y^3
![因式分解:x^3 -3x^2 y + 3xy^2 - y^3](/uploads/image/z/15303047-23-7.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%3Ax%5E3+-3x%5E2+y+%2B+3xy%5E2+-+y%5E3)
x^3 -3x^2 y + 3xy^2 - y^3
=(x^3-y^3)-(3x^2y-3xy^2)
=(x-y)(x^2+xy+y^2)-3xy(x-y)
=(x-y)(x^2+xy+y^2-3xy)
=(x-y)(x^2-2xy+y^2)
=(x-y)(x-y)^2
=(x-y)^3
=(x^3-y^3)-(3x^2y-3xy^2)
=(x-y)(x^2+xy+y^2)-3xy(x-y)
=(x-y)(x^2+xy+y^2-3xy)
=(x-y)(x^2-2xy+y^2)
=(x-y)(x-y)^2
=(x-y)^3