Find the value of (a 2+2ab+2a) (b 2+2ab+2b).
Derived from the fact that A and B are two real numbers of the equation x 2+2x-5 = 0:
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) squared+1/2 (x-y-z) (x-y+z)-z (x+y), where x-y=6 and xy=2 1. Be specific.
Simplify:
1/2(x+y+z) squared+1/2 (x-y-z) (x-y+z)-z (x+y) =1
1/2[(x+y) square +2z(x+y)+z square ]+ 1/2[(x-y) square -z square ]-z(x+y)=]
1/2(x+y) square+1/2(x-y) square =x square +y square.
From x-y=6, xy=2 1, x+y = (x-y)+2xy = 78.
3. Find the value of 2ab-2a 2-4b 2-7 from a 2-ab+2b 2 = 3.
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. If A = 2x 2+3xy-2x-3, B =-x 2+xy+2, and the value of 3A+6B has nothing to do with X, find the value of y..
Solution:
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), where x=-2.
9x+6x？ -3(x-2/3x？ )
=9x+6x？ -3x+2x？
=8x？ +6 times
=8×(-2)? +6×(-2)
=32- 12
=20
6.1/4 (-4x2+2x-8)-(1/2x-1), where x= 1/2.
1/4(-4x？ +2x-8)-( 1/2x- 1)
=-x？ + 1/2x-2- 1/2x+ 1
=-x？ - 1
=-( 1/2)? - 1
=- 1/4- 1
=-5/4
7.3x' y-[2x' y-(2xyz-x' z)-4x' z]-XYZ, where 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
8.(5a 2-3b 2)+(a 2+b 2)-(5a 2+3b 2), where a =- 1 and 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
9,2 (A2B+AB 2)-2 (A2B-1)-2AB 2-2, where a =-2 and b = 2.
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
10 squared, (x-21y-1) (x-21y+1)-(x-21y-1).
Where x = 1.7 and y = 3.9 (simplify first and then evaluate).
[(X-2 is 1Y)- 1][(X+2 is 1Y)+ 1]-(X-2 is1y-0/) square.
= (x+ 1Y) square-1-(x- 1Y) square +2 (x- 1Y)- 1.
= (x+ 1Y) square -(x- 1Y) square +2 (x- 1y) -(X-2
=2XY+2X-Y-2
=3.9*2.4+ 1.4
= 10.76
Cross-cultural evaluation: I have the following requirements.
1 、-9(x-2)-y(x-5)
(1) simplifies the whole equation.
(2) When x=5, find the solution of y.
2、5(9+a)×b-5(5+b)×a
(1) simplifies the whole equation.
(2) When a=5/7, find the value of the formula.
3、62g+62(g+b)-b
(1) simplifies the whole equation.
(2) When g=5/7, find the solution of b.
4、3(x+y)-5(4+x)+2y
(1) simplifies the whole equation.
5 、( x+y)(x-y)
(1) simplifies the whole equation.
6、2ab+a×a-b
(1) simplifies the whole equation.
7、5.6x+4(x+y)-y
(1) simplifies the whole equation.
8、6.4(x+2.9)-y+2(x-y)
(1) simplifies the whole equation.
9 、( 2.5+x)(5.2+y)
(1) simplifies the whole equation.
10、9.77x-(5-a)x+2a
(5a 2-3b 2)+(a 2+b 2)-(5a 2+3b 2), where a =- 1 and 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
2 (A2B+AB 2)-2 (A2B-1)-2AB 2-2 where a =-2 and b = 2.
=2a^2b+2ab^2-2a^2b+2-2ab^2-2
=0
x+7-(-36+8^2)/2=[-(-8x)+7^4]/3*(8^2-6x)
(a-7)-(-98a)+7a=[(3.2*5a)2^5]/ 10
(89/2+5x)+35/6x=[3*(-9+5)+2^3]/5+7x
[3x+(- 189+5^2)/3]/8=52 1/2
4y+[ 1 19*(-5^3y+8/7)-8/3]=22/ 1 1
(3x* 189)+{5*6+[-5/8*(-65*8^3)]+9/2}
7(2x- 1)-3(4x- 1)= 4(3x+2)- 1
(5y+ 1)+( 1-y)=(9y+ 1)+( 1-3y)
[-6(-7^4*8)-4]=x+2
20%+( 1-20%)(320-x)= 320×40%
2(x-2)+2=x+ 1
2(x-2)-3(4x- 1)= 9( 1-x)
1 1x+64-2x = 100-9x
15-(8-5x)=7x+(4-3x)
3(x-7)-2[9-4(2-x)]=22
3/2[2/3( 1/4x- 1)-2]-x = 2
2x+7^2= 157
9x+6x？ -3(x-2/3x？ )
=9x+6x？ -3x+2x？
=8x？ +6 times
=8×(-2)? +6×(-2)
=32- 12
=20
1/4(-4x？ +2x-8)-( 1/2x- 1)
=-x？ + 1/2x-2- 1/2x+ 1
=-x？ - 1
=-( 1/2)? - 1
=- 1/4- 1
=-5/4
3.3ab-4ab+8ab-7ab+ab=______。
4.7x-(5x-5y)-y=______。
5.23 a3 BC 2- 15 ab2c+8 ABC-24 a3 BC 2-8 ABC = _ _ _ _ _ _。
6.-7x 2+6x+ 13 x2-4x-5x 2 = _ _ _ _ _ _。
7.2y+(-2y+5)-(3y+2)=______。
1 1.(2 x2-3xy+4 y2)+(x2+2xy-3 y2)= _ _ _ _ _ _。
12.2 a-(3a-2 b+2)+(3a-4 b- 1)= _ _ _ _ _ _。
13.-6x2-7x2+ 15x2-2x2=______。
14.2 x-(x+3y)-(-x-y)-(x-y)= _ _ _ _ _ _。
16.2 x+2y-[3x-2(x-y)]= _ _ _ _ _ _。
17.5-( 1-x)- 1-(x- 1)= _ _ _ _ _ _。
18.()+(4xy+7x2-y2)= 10x2-xy。
19.(4xy2-2x2y)-( )=x3-2x2y+4xy2+y3。
2 1. Given A=x3-2x2+x-4 and B=2x3-5x+3, calculate a+b = _ _ _ _.
22. given A=x3-2x2+x-4 and B=2x3-5x+3, calculate a-b = _ _ _ _.
23. If a=-0.2 and b=0.5, the value of the algebraic expression -(|a2b|-|ab2|) is _ _ _ _ _.
25. If a polynomial subtracts 3m4-m3-2m+5 to get -2m4-3m3-2m2- 1, then this polynomial is equal to _ _ _ _.
26.-(2 x2-y2)-[2 y2-(x2+2xy)]= _ _ _ _ _ _。
27. If -3a3b2 and 5ax- 1by+2 are similar terms, then x = _ _ _ _ _, and y = _ _ _ _ _.
28.(-y+6+3 y4-y3)-(2 y2-3 y3+y4-7)= _ _ _ _ _ _。
29. The result of simplifying the algebraic expression 4x2-[7x2-5x-3( 1-2x+x2)] is _ _ _ _.
30.2 a-B2+c-D3 = 2a+()-D3 = 2a-D3-()= c-()。
3 1.3a-(2a-3b)+3(a-2b)-b = _ _ _ _ _ _。
32. The simplified algebraic expression x-[y-2x-(x+y)] is equal to _ _ _ _.
33.[5a 2+()a-7]+[()a2-4a+()]= a2+2a+ 1。
34.3x-[y-(2x+y)]=______。
35.Simplify | 1-x+y |-x-y | (where x < 0, y > 0) equals _ _ _ _.
36. It is known that x≤y, x+y-| x+y-| x-y | = _ _ _ _ _
37. Given x < 0 and y < 0, simplify | x+y |-| 5-x-y | = _ _ _.
38.4a2n-an-(3an-2a2n)=______。
39. If you add -3x2y+2x2-3xy-4 to a polynomial, you get.
2x2y+3xy2-x2+2xy，
Then this polynomial is _ _ _ _.
40.-5xm-xm-(-7xm)+(-3xm)=______。
4 1. When a=- 1 and b=-2,
[a-(b-c)]-[-b-(-c-a)]=______。
43. When a=- 1, b= 1 and c=- 1,
-[b-2(-5a)]-(-3b+5c)=______。
44.-2(3x+z)-(-6x)+(-5y+3z)=______。
45.-5an-an+ 1-(-7an+ 1)+(-3an)= _ _ _ _ _ _。
46.3 a-(2a-4 b-6c)+3(-2c+2b)= _ _ _ _ _ _。
48.9 a2+[7 a2-2a-(-a2+3a)]= _ _ _ _ _ _。
50. When 2y-x=5, 5 (x-2y) 2-3 (-x+2y)-100 = _ _ _.
(2) Choose
[ ]
A.2
B.-2;
C.- 10;
D.-6.
52. In the following categories, the calculation result is -7x-5x2+6x3 [].
a . 3x-(5 x2+6 x3- 10x)；
b . 3x-(5 x2+6 x3+ 10x)；
c . 3x-(5 x2-6 x3+ 10x)；
D.3x-(5x2-6x3- 10x)。
53. Combine (-x-y)+3(x+y)-5(x+y) into the same category [].
A.(x-y)-2(x+y)；
B.-3(x+y)；
C.(-x-y)-2(x+y)；
D.3(x+y)。
54.2a-[3b-5a-(2a-7b)] equals []
A.-7a+ 10b；
b . 5a+4b；
C.-a-4b；
D.9a- 10b。
55. The algebraic expression that minus -3m equals 5m2-3m-5 is [].
a . 5(m2- 1)；
b . 5m 2-6m-5；
c . 5(m2+ 1)；
D.-(5m2+6m-5)。
56. The similar terms in the polynomial 2ab-9a2-5ab-4a2 are combined together respectively, which should be [].
A.(9 a2-4a 2)+(-2 ab-5ab)；
B.(9 a2+4a 2)-(2ab-5ab)；
C.(9 a2-4a 2)-(2ab+5ab)；
D.(9a2-4a2)+(2ab-5ab)。
57. When a=2 and b= 1, -a2b+3ba2-(-2a2b) equals [].
A.20
B.24
C.0
D. 16。
(3) simplification
70.(4x2-8x+5)-(x3+3x2-6x+2)。
72.(0.3x 3-x2y+xy2-y3)-(-0.5x 3-x2y+0.3 xy2)。
73.-{2a2b-[3abc-(4ab2-a2b)]}。
74.(5a2b+3a2b 2-ab2)-(-2ab 2+3a2b 2+a2b)。
75.(x2-2 y2-z2)-(-y2+3 x2-z2)+(5x 2-y2+2z 2)。
76.(3 a6-a4+2 a5-4 a3- 1)-(2-a+a3-a5-a4)。
77.(4a-2b-c)-5a-[8b-2c-(a+b)]。
78.(2m-3n)-(3m-2n)+(5n+m)。
79.(3 a2-4 ab-5 B2)-(2 B2-5a 2+2ab)-(-6ab)。
80.xy-(2xy-3z)+(3xy-4z)。
8 1.(-3x 3+2 x2-5x+ 1)-(5-6x-x2+x3)。
83.3x-(2x-4y-6x)+3(-2z+2y)。
84.(-x2+4+3x4-x3)-(x2+2x-x4-5)。
85. If A=5a2-2ab+3b2 and B=-2b2+3ab-a2, calculate a+b. 。
86. It is known that A=3a2-5a- 12, B=2a2+3a-4, and find 2 (a-b).
87.2m-{-3n+[-4m-(3m-n)]}。
88.5m2n+(-2m2n)+2mn2-(+m2n)。
89.4(x-y+z)-2(x+y-z)-3(-x-y-z)。
90.2(x2-2xy+y2-3)+(-x2+y2)-(x2+2xy+y2)。
92.2(a2-a b-B2)-3(4a-2b)+2(7 a2-4a b+B2)。
94.4x-2(x-3)-3[x-3(4-2x)+8]。
(4) Simplify the following categories before evaluating.
97. Given a+b=2 and a-b=- 1, find the value of 3(a+b)2(a-b)2-5(a+b)2×(a-b)2.
98. It is known that A=a2+2b2-3c2, B=-b2-2c2+3a2, C=c2+2a2-3b2, and find (A-B)+C. 。
99.Find (3x2y-2x2y)-(xy2-2x2y), where x=- 1 and y = 2.
10 1. Given |x+ 1|+(y-2)2=0, find the value of algebraic expression 5(2x-y)-3(x-4y).
106. when P=a2+2ab+b2 and Q=a2-2ab-b2, find p-[q-2p-(p-q)].
107. Find the value of 2x2-{-3x+5+[4x2-(3x2-x=-3. 1)], where x =-3.
1 10. When x=-2, y=- 1 and z=3, find the value of 5XYZ-{2x2y-[3xXYZ-(4xy2-x2y)]}.
1 13. Given A=x3-5x2 and B=x2-6x+3, find a-3 (-2b).
(5) Comprehensive exercises
1 15. Remove the brackets: {-[-(a+b)]}-{-[-(a-b)]}.
1 16. Delete the brackets: -[-(-x)-y]-[+(-y)-(+x)].
1 17. Given A=x3+6x-9 and B=-x3-2x2+4x-6, calculate 2A-3B, and put the result in brackets with "-"in front.
1 18. Calculate the following formula and put the result in brackets with "-"in front:
(-7 y2)+(-4y)-(-y2)-(+5y)+(-8 y2)+(+3y)。
1 19. Remove the brackets, merge similar items, and arrange the results according to the ascending power of x, and put the last three items in brackets with "-":
120. Without changing the value of the following formula, change the symbol before each bracket to the opposite symbol: (x3+3x2)-(3x2y-7xy)+(2y3-3y2).
12 1. Put the cubic term of polynomial 4x2y-2xy2+4xy+6-x2y2+x3-y2 in brackets with "-"in front, the quadratic term in brackets with "+"in front, and the quartic term and constant term in brackets with "-"in front.
122. Remove the brackets of the following polynomials, combine similar terms, put them in brackets with "-"in front, and then find the value of 2x-2[3x-(5x2-2x+ 1)]-4x2, where x =- 1.
123. Merge similar projects:
7x- 1.3z-4.7-3.2x-y+2. 1z+5-0. 1y。
124. Merge similar items: 5m2n+5mn2-Mn+3m2n-6mn2-8mn.
126. Remove brackets and merge similar items:
( 1)(m+ 1)-(-n+m)；
(2)4m-[5m-(2m- 1)]。
127. Simplified: 2x2-{-3x-[4x2-(3x2-x)+(x-x2)]}.
128. Simplification:-(7x-y-2z)-{[4x-(x-y-z)-3x+z]-x}.
129. Calculation: (+3a)+(-5a)+(-7a)+(-31a)-(+4a)-(-8a).
130. Simplification: a3-(a2-a)+(a2-a+1)-(1-a4+a3).
13 1. Combine the similar items of x2-8x+2x3- 13x2-2x-2x3+3 and evaluate them, where x =-4.
132. Fill in the appropriate items in brackets: [()-9y+()]+2y2+3y-4 =11y2-()+13.
133. Fill in the appropriate items in brackets:
(-x+y+z)(x+y-z)=[y-( )][y+( )]。
134. Fill in the appropriate items in brackets:
(3x2+xy-7y2)-( )=y2-2xy-x2。
135. Fill in the appropriate items in brackets:
( 1)x2-xy+y- 1 = x2-()；
(2)[()+6x-7]-[4x 2+()-()]= x2-2x+ 1。
136. Calculate the value of 4x2-3 [x+4 (1-x)-x2]-2 (4x2-1).
137. Simplify:
138. Vertical calculation
(-x+5+2x4-6x3)-(3x4+2x2-3x3-7)。
139. a =11x3+8x2-6x+2, B=7x3-x2+x+3, and find 2 (3a-2b).
140. Given A=x3-5x2, B=x3- 1 1x+6, C=4x-3, find.
( 1)A-B-C；
(2)(A-B- China) -(A-B+ China).
14 1. Given A=3x2-4x3 and B=x3-5x2+2, calculate.
( 1)A+B；
(2)B-A。
142. Known x
146. Find the difference between two algebraic expressions-1.56a+3.2a3-0.47, 2.27a3-0.02a2+4.03a+0.53 and 6-0. 15a+3.24a2+5.07a3.
-0.3，y=-0.2。
150. Given (x-3)2+|y+ 1|+z2=0, find the value of x2-2xy-5x2+12xz+3xy-z2-8xz-2x2.