Question

因式分解X^3+Y^3-3XY+1

Answer 1

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