当x-y=1时,那么x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值是?

当x-y=1时,那么x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值是?
当x-y=1时,那么x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值是?

当x-y=1时,那么x^4-xy^3-x^3y-3x^2y+3xy^2+y^4的值是?
x^4-xy^3-x^3y-3x^2y+3xy^2+y^4
=x^4-x^3y+y^4-xy^3-3x^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^2-2xy+y^2
=(x-y)^2
=1
同学,遇到题目要思考啊~

x^4-xy^3-x^3y-3x^2y+3xy^2+y^4
=(x^4-x^3y)-(3x^2y-3xy^2)-(xy^3-y^4)
=x^3(x-y)-3xy(x-y)-y^3(x-y)
=x^3-3xy-y^3
=(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
=1^2
=1