填空（x-y）（x2+xy+y2）=；（x-y）（x3+x2y+xy2+y3）=根据以上等式进行猜想，当n是偶数时，可得：（x-y）（xn+xn-1y+yn-2y2+…+x2yn-2+xyn-1+yn）=．

Question

填空（x-y）（x²+xy+y²）=______；（x-y）（x³+x²y+xy²+y³）=______
根据以上等式进行猜想，当n是偶数时，可得：（x-y）（xⁿ+x^n-1y+y^n-2y²+…+x²y^n-2+xy^n-1+yⁿ）=______．

Answer 1

原式=x3+x2y+xy2-x2y-xy2-y3=x3-y3；故答案为：x3-y3；原式=x4+x3y+x2y2+xy3-x3y-x2y2-xy3-y4=x4-y4；故答案为：x4-y4；原式=xn+1+xny+xyn-2+x2yn-1+xyn-xny-xn-1y2-yn-1y2-…-x2yn-1-xyn-yn+1=xn+1-yn+1，故答案为...