问题 解答题
先化简,再求值:
(1)2(x-y)-3(
1
3
x-2y-1)
,其中x=2011,y=-
1
4

(2)-3(x2-xy)+2(x2+xy-1)+1  其中x=
1
2
,y=-2.
答案

(1)2(x-y)-3(

1
3
x-2y-1)

=2x-2y-x+6y+3

=(2-1)x+(-2+6)y+3

=x+4y+3,

当x=2001,y=-

1
4
时,原式=2011+4×(-
1
4
)+3=2011-1+3=2003;

(2)-3(x2-xy)+2(x2+xy-1)+1

=-3x2+3xy+2x2+2xy-2+1

=(-3+2)x2+(3+2)xy+(-2+1)

=-x2+5xy-1,

当x=

1
2
,y=-2时,原式=-(
1
2
2+5×
1
2
×(-2)-1=-
1
4
-5-1=-
25
4

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