因式分解(x+y)三次方+2xy(1-x-y)-1

问题描述:

因式分解(x+y)三次方+2xy(1-x-y)-1

(x+y)三次方+2xy(1-x-y)-1
=(x+y)三次方-1+2xy(1-x-y)
=(x+y-1)[(x+y)二次方+xy+1]-2xy(x+y-1)
=(x+y-1)[(x+y)二次方-xy+1]
=(x+y-1)(x平方+xy+y平方+1)