1.(20 14? Hengyang) The following operation result is correct ()
A.x2+x3=x5 B.x3？ x2=x6 C.x5？ x=x5 D.x3？ (3x)2=9x5
2. The result of (1+x2) (x2-1) is ().
a . x2- 1 b . x2+ 1 c . x4- 1d . 1-x4
3. Any given non-zero number is calculated according to the following process, and the final output result is ().
m？ Square? -Huh? +2? result
B.m-2 in the morning and C.m+/kloc-0 in the afternoon/m-/kloc-0 in the afternoon/
4. The following calculation error is ()
A.(- 14+4x2)？ 12 =- 12+8 x2 b .(x+2y)(2y-x)=-x2+4 y2
c . x2-9 =(x+3)(x-3)d .(x+y)2-xy = x2+y2
5.(20 14? Hainan) The following formula is decomposed from left to right, which is ()
a . a2+4a-2 1 = a(a+4)-2 1 b . a2+4a-2 1 =(a-3)(a+7)
C.(a-3)(a+7)= a2+4a-2 1d . a2+4a-2 1 =(a+2)2-25
6. The following polynomials can be decomposed by formula () within the range of real numbers.
①x2+6x+9； ②4x 2-4x- 1； ③-x2-y2； ④2 x2-y2； ⑤x2-7； ⑥9x2 +6xy+4y2。
A.3 B.4 C.5 D.6
7. If (a+b)2=(a-b)2+A, then A is ().
A.2ab B.-2ab C.4ab D.-4ab
8. If the calculation result of (x2-3x+n)(x2+mx+8) does not contain the items of x2 and x3, then the values of m and n are ().
A.m=3，n= 1 B.m=0，n=0 C.m=-3，n=-9 D.m=-3，n=8
9. If a, b and c are three sides of a triangle, then the algebraic expression (a-b) 2-the value of C2 ().
A. greater than 0 b. less than 0 c. equal to 0 d. uncertain.
10.7 the picture shown in figure ① is a long and b wide (a >；; B) Put the rectangular pieces of paper into the rectangular ABCD without overlapping as shown in Figure ②, and the uncovered parts (two rectangles) are indicated by shading. Let the difference between the areas of the shadow in the upper left corner and the lower right corner be s, and when the length of BC changes, it is also placed, and S remains unchanged, then A and B satisfy ().
A.a=52b B.a=3b
C.a=72b D.a=4b
Fill in the blanks (3 points for each small question, 24 points for * * *)
1 1.(20 14? Shaanxi) factorization: m (x-y)+n (y-x) = _ _ _ _ _ _ _.
12. Calculation: |-3|+ (? + 1)0-4=________.
13. Calculate 820 14? (-0. 125)20 15=________.
14.(20 14? Lianyungang) If ab=3, a-2b=5, A2B-2AB 2 = _ _ _ _ _ _
15. Given x=y+4, the value of the algebraic expression x2-2xy+y2-25 is _ _ _ _ _ _ _ _.
16. If 6a=5, 6b=8, 36a-b = _ _ _ _ _ _
17. Mathematicians invented a magic box. When any number pair (a, b) inputs it, it will get a new number: (a- 1)(b-2). Now put the number pair (m, 1) in to get the number n, and then put the number pair (n, m) in.
18. Use 1 A? A square, 1 B? B's square and two A's? B's rectangles can be spliced into squares (as shown in the figure), so that the formula of factorization can get _ _ _ _ _ _ _ _ _ _ _ _.
Iii. Answering questions (***66 points)
19.( 12 points) Calculation:
( 1)5x2y？ (- 13xy)？ (2xy 2)2；
(2)9(a- 1)2-(3a+2)(3a-2)；
(3)[(a-2b)2+(a-2b)(2 b+ a)-2a(2a-b)]？ 2a；
(4)[a(a2b2-ab)-b(-a3b-a2)]？ a2b
20.(9 points) Decompose the following factors:
( 1)x(m-x)(m-y)-m(x-m)(y-m)； (2)ax2+8ax+ 16a；
(3)x4-8 1x2y2。
2 1.(6 points) Given xm=3 and xn=2, find the value of x3m+2n.
22.(9 points) Given x(x- 1)-(x2-y)=-6, find the value of x2+y22-xy.
23.(8 points) After learning the knowledge of factorization, the teacher raised such a question: If n is an integer, can the value of (n+7)2-(n-3)2 be divisible by 20? If yes, please explain the reasons; If not, please give a counterexample. Can you answer this question?
24.( 10) As shown in the figure, a city has a rectangular plot, which is (3a+b) meters long and (2a+b) meters wide. The planning department plans to green the shadow and build a statue in the middle. How big is the green area? And calculate the green area when a=3 and b=2.
25.( 12 point) Observe the following equation:
12? 23 1= 132? 2 1,
13? 34 1= 143? 3 1,
23? 352=253? 32,
34? 473=374? 43,
62? 286=682? 26,
?
The numbers on both sides of each equation are symmetrical respectively, and there are the same rules between the numbers that make up two digits and three digits in each equation. We call this equation. Digital symmetry equation? .
(1) Fill in the blanks according to the law reflected above, so that the formula becomes? Digital symmetry equation? ：
①52? ________=________? 25; ②________? 396=693? ________.
(2) Let the tenth digit of the two digits on the left of this equation be A, and the single digit be B, 2? a+b？ 9. Write a statement? Digital symmetry equation? The formula of general law (including A and B), and prove it.
Chapter 14 Reference answers to test questions
1.D 2。 C 3。 C 4 explosive D 5。 B 6。 A seven. C 8。 A nine. B 10。 B 1 1。 (x-y)(m-n) 12.2 13。 - 18 14. 15 15.-9 16.2564 17.2m-m2 18 . a2+2ab+B2 =(a+b)2
19.( 1) Original formula =5x2y? (- 13xy)？ 4x2y4=-(5？ 13? 4) x2-1+2y1-1+4 =-60x3y4 (2) Original formula = 9 (a2-2a+1)-(9a2-4) = 9a2-/kloc-0. 2a=2a(a-2b-2a+b)？ 2a=-a-b (4) Original formula =(a3b2-a2b+a3b2+a2b)? a2b=2a3b2？ a2b=2ab
20.( 1) The original formula = x (m-x) (m-y)-m (m-x) (m-y) = (m-y) (x-m) =-(m-x) 2 (m-y).
2 1.xm = 3，xn=2，？ Original formula =(xm)3? (xn)2=33？ 22= 108
22.x-y=6 from x(x-1)-(x2-y)=-6, x2+y22-xy=x2-2xy+y22=(x-y)22, substitute x-y=6 to get 622 = 65438+.
23.(n+7)2-(n-3)2 =(n+7+n-3)(n+7-n+3)=(2n+4)？ 10=20(n+2)，？ It must be divisible by 20.
24. The green area is: (3a+b) (2a+b)-(a+b) 2 = 6a2+5ab+b2-(a2+2ab+b2) = 5a2+3ab (square meter). When a=3 and b=2, 5a2+3ab=5? 32+3? 3? 2=45+ 18=63. Answer: The green area is (5a2+3ab) square meters. When a=3 and b=2, the green area is 63 square meters.
25.( 1)275; 572; 63; 36 (1)∵ The ten digits of the two digits on the left are A, and the single digits are B,? The two bits on the left are 10a+b, the three bits are10b+/kloc-0 (a+b)+a, the two bits on the right are 10b+a, and the three bits are100a+10. The general formula is: (10a+b)? [ 100 b+ 10(a+b)+a]=[ 100 a+ 10(a+b)+b]？ (10b+a), proof: left =( 10a+b)? [ 100 b+ 10(a+b)+a]=( 10a+b)( 10b+ 10a+ 10b+a)=( 10a+)( 10b+a)=( 10a+ 10b+b)( / kloc-0/0b+a)=( 10 b)[ 100 b+ 10(a+b)+a]=[ 100 a+ 10(a+b)+b]？ ( 10b+a)