当x-y=1时,那么x4-xy3-x3y-3x2y+3xy2+y4的值是( )A. -1B. 0C. 1D. 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
答
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...
答案解析:本题应对代数式进行化简,得出含有x-y的式子,再将x-y=1代入即可.
考试点:因式分解的应用.
知识点:本题考查了因式分解的应用;解题的关键是整体代换的思想.