更新時(shí)間:2024-01-12 16:29:18作者:貝語(yǔ)網(wǎng)校
當(dāng)x-y=1時(shí),那么x4-xy3-x3y-3x2y+3xy2+y4的值是
A.-1
B.0
C.1
D.2
C
本題應(yīng)對(duì)代數(shù)式進(jìn)行化簡(jiǎn),得出含有x-y的式子,再將x-y=1代入即可.
解答: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×(x2+xy+y2)-3xy]
=x2-2xy+y2=(x-y)2
∵x-y=1,
∴原式=1.
故選C.
點(diǎn)評(píng):本題考查了因式分解的應(yīng)用;解題的關(guān)鍵是整體代換的思想.