已知x-y=1 求代数式x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值 20
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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)
而x-y=1
=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)
而x-y=1
=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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