Question

因式分解(x+y)³+2xy(1-x-y)-1

最好是有过程...谢谢

Answer 1

原式=[(x+y)³-1]+2xy(1-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)

Answer 2

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