当x-y=1,求x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值
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当x-y=1,求x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值
![当x-y=1,求x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值](/uploads/image/z/3881959-7-9.jpg?t=%E5%BD%93x-y%3D1%2C%E6%B1%82x%5E4-xy%5E3-x%5E3y-3x%5E2y%2B3xy%5E2%2By%5E4%E7%9A%84%E5%80%BC)
x^4-xy^3-x^3y-3x^2y+3xy^2+y^4
=(x^4-x^3y)-xy^3+y^4-3x^2y+3xy^2
=x^3(x-y)-y^3(x-y)-3xy(x-y)
=x^3-y^3-3xy
=(x-y)(x^2+xy+y^2)-3xy
=x^2+xy+y^2-3xy
=x^2-2xy+y^2
=(x-y)^2
=1
=(x^4-x^3y)-xy^3+y^4-3x^2y+3xy^2
=x^3(x-y)-y^3(x-y)-3xy(x-y)
=x^3-y^3-3xy
=(x-y)(x^2+xy+y^2)-3xy
=x^2+xy+y^2-3xy
=x^2-2xy+y^2
=(x-y)^2
=1
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