若x+y=-1,则x4+5x3y+x2y+8x2y2+xy2+5xy3+y4的值等于( )
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若x+y=-1,则x4+5x3y+x2y+8x2y2+xy2+5xy3+y4的值等于( )
A. 0
B. -1
C. 1
D. 3
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+y2)-3xy],
=(x2-xy+y2)+3xy,
=(x+y)2-3xy+3xy,
=1.
故选C.
=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.
若x+y=-1,则x4+5x3y+x2y+8x2y2+xy2+5xy3+y4的值等于( )
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