当x-y=1时,那么x4-xy3-x3y-3x2y+3xy2+y4的值是(  ) A.-1 B.0 C.1 D.2

问题描述:

当x-y=1时,那么x4-xy3-x3y-3x2y+3xy2+y4的值是(  )
A. -1
B. 0
C. 1
D. 2

x4-xy3-x3y-3x2y+3xy2+y4=(x4-xy3)+(y4-x3y)+(3xy2-3x2y)=x(x3-y3)+y(y3-x3)+3xy(y-x)=(x3-y3)(x-y)-3xy(x-y)=(x-y)(x3-y3-3xy)=(x-y)[(x-y)(x2+xy+y2)-3xy]把x-y=1代入得,原式=1×[1...