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

问题描述:

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

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...