已知x-y=1,则x^4-x^3y-xy^3-3x^2y+3xy^2+y^4=

已知x-y=1,则x^4-x^3y-xy^3-3x^2y+3xy^2+y^4=
已知x-y=1,则x^4-x^3y-xy^3-3x^2y+3xy^2+y^4=

已知x-y=1,则x^4-x^3y-xy^3-3x^2y+3xy^2+y^4=
x^4-x^3y-xy^3-3x^2y+3xy^2+y^4
=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