问题 解答题
(1)化简并求值:
1
2
a-[4b-c-(
1
2
a-c)]+[6a-(b-c)],其中a=0.1,b=0.2,c=0.3;
(2)已知A=2x-3y+1,B=3x+2y,求2A-B;
(3)若m-n=4,mn=-1,求(-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)的值.
答案

(1)

1
2
a-[4b-c-(
1
2
a-c)]+[6a-(b-c)]

=

1
2
a-4b+c+(
1
2
a-c)+6a-(b-c)

=

1
2
a-4b+c+
1
2
a-c+6a-b+c

=7a-5b+c

当a=0.1,b=0.2,c=0.3时,

原式=7×0.1-5×0.2+0.3=0;

(2)∵A=2x-3y+1,B=3x+2y

∴2A-B=2(2x-3y+1)+2(3x+2y)

=4x-6y+2+6x+4y

=x-8y+2;

(3)∵m-n=4,mn=-1

∴(-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)

=-2mn+2m+3n-3mn-2n+2m-m-4n-mn

=-6mn+3(m-n)

当m-n=4,mn=-1时,

原式=-6×(-1)+3×4=18.

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