（x-y)()=x^2-y^2(x-y)(x^2+xy+y^2)=(x-y)(x^3+x^2y+xy^2+y^3=(x-y)()=x^5-y^5……根据以上结果,你发现什么规律,请继续填空（x-y)(x^n+x^n-1+x^n-2y^2+……+x^2y^n-2+xy^n-1+y^n)=

Question

（x-y)(______)=x^2-y^2 (x-y)(x^2+xy+y^2)=________ (x-y)(x^3+x^2y+xy^2+y^3=________
(x-y)(__________)=x^5-y^5
……
根据以上结果,你发现什么规律,请继续填空
（x-y)(x^n+x^n-1+x^n-2y^2+……+x^2y^n-2+xy^n-1+y^n)=_____________

Answer 1

（x-y)(___x+y___)=x^2-y^2 (x-y)(x^2+xy+y^2)=____x³-y³____ (x-y)(x^3+x^2y+xy^2+y^3=__x^4-y^4______
x-y)(____x^4+x³y+x²y²+xy³+y^4______)=x^5-y^5
……
根据以上结果,你发现什么规律,请继续填空（x-y)(x^n+x^n-1+x^n-2y^2+……+x^2y^n-2+xy^n-1+y^n)=______x^(n+1)-y^(n+1)_______