若x+y=-1,则x4+5x3y+x2y+8x2y2+xy2+5xy3+y4的值等于(  ) A.0 B.-1 C.1 D.3

若x+y=-1,则x4+5x3y+x2y+8x2y2+xy2+5xy3+y4的值等于(  )
A. 0
B. -1
C. 1
D. 3
数学人气:863 ℃时间:2019-08-21 21:02:08
优质解答
原式=x4+x3y+4x3y+x2y+4x2y2+4x2y2+xy2+4xy3+xy3+y4
=x3(x+y)+4x2y(x+y)+xy(x+y)+4xy2(x+y)+y3(x+y),
=-x3-4x2y-xy-4xy2-y3
=-[(x3+y3)+4xy(x+y)+xy],
=-[(x+y)(x2-xy+y2)-4xy+xy],
=-[-(x2-xy+y2)-3xy],
=(x2-xy+y2)+3xy,
=(x+y)2-3xy+3xy,
=1.
故选C.
我来回答
类似推荐
请使用1024x768 IE6.0或更高版本浏览器浏览本站点,以保证最佳阅读效果。本页提供作业小助手,一起搜作业以及作业好帮手最新版!
版权所有 CopyRight © 2012-2024 作业小助手 All Rights Reserved. 手机版