因式分解(x+y)^3+2xy-2x^2y-2xy^2-1

(x+y)^3+2xy-2x^2y-2xy^2-1=(x+y)^3-1+2xy-2xy(x+y)+2xy-1=(x+y-1)[(x+y)²+(x+y)+1]-2xy(x+y-1)=(x+y-1)(x²+2xy+y²+x+y+1-2xy)=(x+y-1)(x²+y²+x+y+1) 再问： 貌似。。错了吧。。 (x+y)^3+2xy-2x^2y-2xy^2-1==(x+y)^3-1+2xy-2xy(x+y)+2xy-1吗? 再答： 多写了一个2xy-1，是抄错的 (x+y)^3+2xy-2x^2y-2xy^2-1 =(x+y)^3-1+2xy-2xy(x+y) =(x+y-1)[(x+y)²+(x+y)+1]-2xy(x+y-1) =(x+y-1)(x²+2xy+y²+x+y+1-2xy) =(x+y-1)(x²+y²+x+y+1)