Question

化简求值题及答案40道

化简求值题及答案40道

Answer 1

化简求值题及答案推荐如下：

1、已知A,B是方程x^2+2x-5=0的两个实数根, 

求(A^2+2AB+2A)(B^2+2AB+2B)的值. 

由A,B是方程x^2+2x-5=0的两个实数根得： 

AB=-5，A+B=-2 

A^2+2AB+2A)(B^2+2AB+2B) 

=AB（A+2B+2）（B+2A+2） 

=-5（-2+B+2）（-2+A+2） 

=-5AB 

=25 

2、1/2(x+y+z)方+1/2(x-y-z)(x-y+z)-z(x+y),其中x-y=6,xy=21.要详细步骤 

化简得： 

1/2(x+y+z)方+1/2(x-y-z)(x-y+z)-z(x+y)= 

1/2[(x+y)方+2z(x+y)+z方]+1/2[(x-y)方-z方]-z(x+y)= 

1/2(x+y)方+1/2(x-y)方=x方＋y方 

由x-y=6,xy=21得，x方＋y方＝（x-y）方＋2xy＝78 

3、a^2-ab+2b^2=3 求2ab-2a^2-4b^2-7的值

2ab-2a^2-4b^2-7 

=2(ab-a^2-2b^2)-7 

=-2(a^2-ab+2b^2)-7 

=(-2)*3-7 

=-6-7=-13 

4、若A=2x^2+3xy-2x-3,B=-x^2+xy+2,且3A+6B的值与x无关，求y的值

解： 

3A+6B=6x^2+9xy-6x-9-6x^2+6xy+12 

=15xy-6x+3 

=x(15y-6)+3 

5、9x+6x^2 -3(x-2/3x^2).其中x=-2 

9x+6x² -3(x-2/3x²) 

=9x+6x²-3x+2x² 

=8x²+6x 

=8×(-2)²+6×(-2) 

=32-12 

=20 

6、1/4(-4x^2+2x-8)-(1/2x-1),其中x=1/2 

1/4(-4x²+2x-8)-(1/2x-1) 

=-x²+1/2x-2-1/2x+1 

=-x²-1 

=-(1/2)²-1 

=-1/4-1 

=-5/4 

7、3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz,其中x=-2,y=-3,z=1, 

:3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz 

=3x'y-2x'y+2xyz-x'z+4x'z-xyz 

=x'y-xyz+3x'z 

=4*(-3)-2*3*1+3*4*1 

=-12-6+12 

=-6 

Answer 2

1,3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz,其中x=-2,y=-3,z=1,
原式=3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
当x=2,y=3,z=1时
原式=4*(-3)-2*3*1+3*4*1
=-12-6+12
=-6
2,3X+2Y)+(4X+3Y)其中X=5,Y+3
原式=3X+2Y+4X+3Y=7X+5Y
当X=5,Y=3时
原式=5*7+（-3）*5+20
=35-15+20
=40
3,2x-3(2x-x)+(2y-y),其中x=1,y=2
解；原式=2x-3x+y
当x=1,y=2时
原式=2*1-3*1+2
=2-3+2
=1
4,(5a^2-3b^2)+(a^2+b^2)-(5a^2+3b^2),其中a=-1,b=1
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(-1)^2-5*1^2
=1-5
=-4
5,2(a^2b+ab^2)-2(a^2 b-1)-2ab^2 -2其中a=-2,b=2
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0,
6,a^2-ab+2b^2=3 求2ab-2a^2-4b^2-7的值
2ab-2a^2-4b^2-7
=2(ab-a^2-2b^2)-7
=-2(a^2-ab+2b^2)-7
=(-2)*3-7
=-6-7
=-13
7,若A=2x^2+3xy-2x-3,B=-x^2+xy+2,且3A+6B的值与x无关,求y的值
3A+6B=6x^2+9xy-6x-9-6x^2+6xy+12
=15xy-6x+3
=x(15y-6)+3
8,x+6x^2 -3(x-2/3x^2).其中x=-2
9x+6x² -3(x-2/3x²)
=9x+6x²-3x+2x²
=8x²+6x
=8×(-2)²+6×(-2)
=32-12
=20
9,1/4(-4x^2+2x-8)-(1/2x-1),其中x=1/2
1/4(-4x²+2x-8)-(1/2x-1)
=-x²+1/2x-2-1/2x+1
=-x²-1
=-(1/2)²-1
=-1/4-1
=-5/4,
10,3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz,其中x=-2,y=-3,z=1,
:3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
=4*(-3)-2*3*1+3*4*1
=-12-6+12
=-6
11,(5a^2-3b^2)+(a^2+b^2)-(5a^2+3b^2),其中a=-1,b=1
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(-1)^2-5*1^2
=1-5
=-4
12、2(a^2b+ab^2)-2(a^2 b-1)-2ab^2 -2其中a=-2,b=2
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
13、(X-2分之1Y-1)(X-2分之1Y+1)-(X-2分之1Y-1)的平方,其中X=1.7,Y=3.9
[(X-2分之1Y)-1][(X+2分之1Y)+1]-(X-2分之1Y-1)平方
=(X+2分之1Y)平方-1-(X-2分之1Y)平方+2(X-2分之1Y)-1
=(X+2分之1Y)平方-(X-2分之1Y)平方+2(X-2分之1Y)-2
=2XY+2X-Y-2
=3.9*2.4+1.4
=10.76
14,2a-（3a-2b+2）+（3a-4b-1),其中a=5 b=-3
=2a-3a+2b-2+3a-4b-1
=（2-3+3）a+（2-4）b+（-2-1）
=2a-2b-3
=10-(-6)-3
=10+6-3
=13
15,5-(1-x)-1-(x-1）-2x+(-5y）,其中x=2,y=2x
=4-2x-5y
=4-4-20
=-20
16,2x-(x+3y)-(-x-y)-(x-y),其中x=3,y=-3
=2x-x+3y+x+y-x+y
=x+5y
=3-15
=-12
17,-ab+3ba-(-2ab),其中a=2,b=1
=-ab+3ba+2ab
=2ab+2ab
=4ab
=4*2*1
=8
18,-m-[-(2m-3n)]+[-(-3m)-4n],其中m=2,n=1
=-m-(-2m+3n)+3m-4n
=-m-4m+2m-3n+3m
=-3n
=-3*1
=-3
19,2（2a+2ab)-2(2ab-1)-2ab-2,其中a=-2 b=2
=4a+4ab-4ab+2-2ab-2
=4a-2ab
=4*(-2)-2*(-2)*2
=-8-(-8)
=8+8
=0
20,3ab-4ab+8ab-7ab+ab,其中a=-2,b=3
=-8ab+9ab
=ab
=-2*3
=-6

Answer 3

1,3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz,其中x=-2,y=-3,z=1,
原式=3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
当x=2,y=3,z=1时
原式=4*(-3)-2*3*1+3*4*1
=-12-6+12
=-6
2,3X+2Y)+(4X+3Y)其中X=5,Y+3
原式=3X+2Y+4X+3Y=7X+5Y
当X=5,Y=3时
原式=5*7+（-3）*5+20
=35-15+20
=40
3,2x-3(2x-x)+(2y-y),其中x=1,y=2
解；原式=2x-3x+y
当x=1,y=2时
原式=2*1-3*1+2
=2-3+2
=1
4,(5a^2-3b^2)+(a^2+b^2)-(5a^2+3b^2),其中a=-1,b=1
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(-1)^2-5*1^2
=1-5
=-4
5,2(a^2b+ab^2)-2(a^2 b-1)-2ab^2 -2其中a=-2,b=2
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0,
6,a^2-ab+2b^2=3 求2ab-2a^2-4b^2-7的值
2ab-2a^2-4b^2-7
=2(ab-a^2-2b^2)-7
=-2(a^2-ab+2b^2)-7
=(-2)*3-7
=-6-7
=-13
7,若A=2x^2+3xy-2x-3,B=-x^2+xy+2,且3A+6B的值与x无关,求y的值
3A+6B=6x^2+9xy-6x-9-6x^2+6xy+12
=15xy-6x+3
=x(15y-6)+3
8,x+6x^2 -3(x-2/3x^2).其中x=-2
9x+6x² -3(x-2/3x²)
=9x+6x²-3x+2x²
=8x²+6x
=8×(-2)²+6×(-2)
=32-12
=20
9,1/4(-4x^2+2x-8)-(1/2x-1),其中x=1/2
1/4(-4x²+2x-8)-(1/2x-1)
=-x²+1/2x-2-1/2x+1
=-x²-1
=-(1/2)²-1
=-1/4-1
=-5/4,
10,3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz,其中x=-2,y=-3,z=1,
:3x'y-[2x'y-(2xyz-x'z)-4x'z]-xyz
=3x'y-2x'y+2xyz-x'z+4x'z-xyz
=x'y-xyz+3x'z
=4*(-3)-2*3*1+3*4*1
=-12-6+12
=-6
11,(5a^2-3b^2)+(a^2+b^2)-(5a^2+3b^2),其中a=-1,b=1
=5a^2-3b^2+a^2+b^2-5a^2-3b^2
=a^2-5b^2
=(-1)^2-5*1^2
=1-5
=-4
12、2(a^2b+ab^2)-2(a^2 b-1)-2ab^2 -2其中a=-2,b=2
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
13、(X-2分之1Y-1)(X-2分之1Y+1)-(X-2分之1Y-1)的平方,其中X=1.7,Y=3.9
[(X-2分之1Y)-1][(X+2分之1Y)+1]-(X-2分之1Y-1)平方
=(X+2分之1Y)平方-1-(X-2分之1Y)平方+2(X-2分之1Y)-1
=(X+2分之1Y)平方-(X-2分之1Y)平方+2(X-2分之1Y)-2
=2XY+2X-Y-2
=3.9*2.4+1.4
=10.76
14,2a-（3a-2b+2）+（3a-4b-1),其中a=5 b=-3
=2a-3a+2b-2+3a-4b-1
=（2-3+3）a+（2-4）b+（-2-1）
=2a-2b-3
=10-(-6)-3
=10+6-3
=13
15,5-(1-x)-1-(x-1）-2x+(-5y）,其中x=2,y=2x
=4-2x-5y
=4-4-20
=-20
16,2x-(x+3y)-(-x-y)-(x-y),其中x=3,y=-3
=2x-x+3y+x+y-x+y
=x+5y
=3-15
=-12
17,-ab+3ba-(-2ab),其中a=2,b=1
=-ab+3ba+2ab
=2ab+2ab
=4ab
=4*2*1
=8
18,-m-[-(2m-3n)]+[-(-3m)-4n],其中m=2,n=1
=-m-(-2m+3n)+3m-4n
=-m-4m+2m-3n+3m
=-3n
=-3*1
=-3
19,2（2a+2ab)-2(2ab-1)-2ab-2,其中a=-2 b=2
=4a+4ab-4ab+2-2ab-2
=4a-2ab
=4*(-2)-2*(-2)*2
=-8-(-8)
=8+8
=0
20,3ab-4ab+8ab-7ab+ab,其中a=-2,b=3
=-8ab+9ab
=ab
=-2*3
=-6

Answer 4

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