X³+3XY+Y³-1的因式分解

X^3+3xy+y^3-1
=x^3+3x^2y+3xy^2+y^3-3x^2y-3xy^2+3xy-1
=(x+y)^3-1+3xy(1-x-y)
=(x+y-1)〔(x+y)^2+(x+y)+1〕+3xy(1-x-y)
=(x+y-1)(x^2-xy+y^2+x+y+1)

x3+3xy+y3-1
=(x+y)3-3x2y-3xy2+3xy-1 添项 （x+y)3=~
=[(x+y)3-1]-3xy(x+y-1) 合并同类项
=(x+y-1){[(x+y)2-(x+y)+1]-3xy}合并同类项
=~~~~~
剩下的没问题了吧！