因式分解(x+y)立方+2xy-2x平方y-2xy平方-1

Question

因式分解(x+y)立方+2xy-2x平方y-2xy平方-1

Answer 1

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