Junior high school second grade mathematics examination paper

1- 14 x2

4x–2 x2–2

(x-y)3-(y-x)

x2–y2–x+y

x2–y2- 1(x+y)(x–y)

x2 + 1 x2 -2-( x - 1x )2

a3-a2-2a

4m2-9n2-4m+ 1

3a2+bc-3ac-ab

9 x2+2xy-y2

2x2-3x- 1

-2x2+5xy+2y2

10a(x-y)2-5b(y-x)

An+1-4an+4an- 1

x3(2x-y)-2x+y

x(6x- 1)- 1

2ax- 10ay+5by+6x

1-a2-ab- 14 b2

a4+4

(x2+x)(x2+x-3)+2

x5y-9xy5

-4x2+3xy+2y2

4a-a5

2x2-4x+ 1

4y2+4y-5

3X2-7X+2

8xy(x-y)-2(y-x)3

x6-y6

x3+2xy-x-xy2

(x+y)(x+y- 1)- 12

4ab-( 1-a2)( 1-b2)

-3 square meters -2 meters +4

a2-a-6

2(y-z)+8 1(z-y)

9m2-6m+2n-n2

ab(c2+d2)+cd(a2+b2)

a4-3a2-4

x4+4y4

a2+2ab+b2-2a-2b+ 1

x2-2x-4

4x2+8x- 1

2x2+4xy+y2

-m2–N2+2mn+ 1

(a+b)3d–4(a+b)2cd+4(a+b)c2d

(x+a)2-(x–a)2

–x5y–xy+2x3y

X6–x4–x2+ 1

(x+3)(x+2)+x2–9

(x–y)3+9(x–y)–6(x–y)2

(a2+B2– 1)2–4a2b 2

(ax+by)2+(bx–ay)2

x2+2ax–3 a2

3a3b2c-6a2b2c2+9ab2c3

xy+6-2x-3y

x2(x-y)+y2(y-x)

2x2-(a-2b)x-ab

a4-9a2b2

ab(x2-y2)+xy(a2-b2)

(x+y)(a-b-c)+(x-y)(b+c-a)

a2-a-b2-b

(3a-b)2-4(3a-b)(a+3b)+4(a+3b)2

(a+3)2-6(a+3)

(x+ 1)2(x+2)-(x+ 1)(x+2)2

35. Factorization x2-25 =.

36. Factorization x2-20x+ 100 =.

37. Factorization x2+4x+3 =.

38. Factorization 4x2- 12x+5 =.

39. Break down the following categories:

( 1)3ax2-6ax= .

(2)x(x+2)-x= .

(3)x2-4x-ax+4a= .

(4)25x2-49= .

(5)36x2-60x+25= .

(6)4x2+ 12x+9= .

(7)x2-9x+ 18= .

(8)2x2-5x-3= .

(9) 12x2-50x+8= .

40. Factorization (x+2) (x-3)+(x+2) (x+4) =.

4 1. Factorization 2ax2-3x+2ax-3 =.

42. Factorize 9X2-66x+ 12 1 =.

43. Factorization 8-2x2 =.

44. Factorization x2-x+ 14 =.

45. Factorization 9X2-30x+25 =.

46. Factorization -20x2+9x+20 =.

47. Factorization 12x2-29x+ 15 =.

48. Factorization is 36x2+39x+9 =.

49. Factorization 2 1x2-3 1x-22 =.

50. Factorization 9x4-35x2-4 =.

5 1. Factorization (2x+1) (x+1)+(2x+1) (x-3) =.

52. Factorization 2ax2-3x+2ax-3 =.

53. Factorize X (y+2)-X-Y- 1 =.

54. Factorization (x2-3x)+(x-3) 2 =.

55. Factorize 9X2-66x+ 12 1 =.

56. Factorization 8-2x2 =.

57. Factorize x4- 1 =.

58. Factorization x2+4x-xy-2y+4 =.

59. Factorization 4x2- 12x+5 =.

60. Factorization 2 1x2-3 1x-22 =.

6 1. Factorization 4x2+4xy+y2-4x-2y-3 =.

62. Factorization 9X5-35x3-4x =.

63. Break down the following categories:

( 1)3x2-6x= .

(2)49x2-25= .

(3)6x2- 13x+5= .

(4)x2+2-3x= .

(5) 12x2-23x-24= .

(6)(x+6)(x-6)-(x-6)= .

3(x+2)(x-5)-(x+2)(x-3)= .

(8)9x2+42x+49= .

( 1)(x+2)-2(x+2)2= .

(2)36x2+39x+9= .

(3)2x 2+ax-6x-3a = 1 .

(4)22x2-3 1x-2 1= .

70. Factorization 3ax2-6ax= =.

7 1. Factorization (x+ 1) x-5x =.

72. Factorization (2x+1) (x-3)-(2x+1) (x-5) =1

73. Factorization xy+2x-5y- 10 =

74. Factorization X2Y2-X2-Y2-6xy+4 =

x3+2x2+2x+ 1

a2b2-a2-b2+ 1

( 1)3ax2-2x+3ax-2

(x2-3x)+(x-3)2+2x-6

1)(2x+3)(x-2)+(x+ 1)(2x+3)

9x2-66x+ 12 1

17. Factorization

( 1)8 x2- 18(2)x2-(a-b)x-ab

18. Break down the following categories

( 1)9 x4+35 x2-4(2)x2-y2-2yz-z2

(3)a(b2-c2)-c(a2-b2)

19. Factorization (2x+1) (x+1)+(2x+1) (x-3)

20. Factorization 39x2-38x+8

2 1. Find the value of (65 12) 2-(34 12) 2 by factorization.

22. Decomposition A (B2-C2)-C (A2-B2)

24. Factorization 7 (x-1) 2+4 (x-1) (y+2)-20 (y+2) 2.

25. decompose xy2-2xy-3x-y2-2y- 1

26. Factorization 4x2-6ax+ 18a2

27. decompose 20a3bc-9a2bc-20ab3c

28. Factorization 2 x2-5x+2ax-5

29. Factorization 4x3+4x2-25x-25

30. Factorization (1-xy) 2-(y-x) 2

3 1. factorization

( 1)mx2-m2-x+ 1(2)a2-2ab+B2- 1

32. Break down the following categories

( 1)5x 2-45(2)8 1x 3-9x(3)x2-y2-5x-5y(4)x2-y2+2yz-z2

33. Factorization: xy2-2xy-3x-y2-2y- 1

34. Factorize Y2 (x-y)+Z2 (y-x)

1) factorization x2+x+y2-y-2xy =

Factorization exercise

First, fill in the blanks:

2.(a-3)(3-2a)= _ _ _ _ _ _ _(3-a)(3-2a)；

12. if m2-3m+2 = (m+a) (m+b), then a = _ _ _ _ _ _ and b = _ _ _ _ _ _

15. When m = _ _ _ _ _, x2+2 (m-3) x+25 is completely flat.

Second, multiple-choice questions:

1. Among the following factorization results, the correct one is

[ ]

A.a2b+7ab-b=b(a2+7a)

b . 3x2y-3xy-6y = 3y(x-2)(x+ 1)

C.8xyz-6x2y2=2xyz(4-3xy)

D.-2a2+4ab-6ac=-2a(a+2b-3c)

2. The factorization factor of polynomial m (n-2)-m2 (2-n) is equal to

[ ]

A.(n-2)(m+m2) B.(n-2)(m-m2)

(n-2)(m+ 1)d(n-2)(m- 1)

3. In the following equation, belongs to the factorization is

[ ]

A.a(x-y)+b(m+n)=ax+bm-ay+bn

b . a2-2ab+B2+ 1 =(a-b)2+ 1

C.-4a2+9b2=(-2a+3b)(2a+3b)

D.x2-7x-8=x(x-7)-8

4. In the following types, factors can be decomposed by square difference formula.

[ ]

A.a2+b2 B.-a2+b2

C.-a2-b2 D.-(-a2)+b2

5. If 9X2+Mxy+ 16Y2 is a completely flat mode, the value of m is

[ ]

A.- 12 B. 24

C. 12

6. By decomposing the polynomial an+4-an+ 1

[ ]

(a4-a) B.an- 1(a3- 1)

c . an+ 1(a- 1)(a2-a+ 1)d . an+ 1(a- 1)(a2+a+ 1)

7. if A2+A =- 1, the value of A4+2A3-3A2-4A+3 is

[ ]

a8b . 7

c 10d 12

8. Assuming that x2+y2+2x-6y+ 10 = 0, the values of x and y are respectively

[ ]

A.x= 1，y=3 B.x= 1，y=-3

C.x=- 1，y=3 D

9. Factorization (m2+3m) 4-8 (m2+3m) 2+ 16.

[ ]

A.(m+ 1)4(m+2)2 b .(m- 1)2(m-2)2(m2+3m-2)

C.(m+4)2(m- 1)2d .(m+ 1)2(m+2)2(m2+3m-2)2

10. Factorization X2-7x-60 is obtained.

[ ]

A.(x- 10)(x+6)b .(x+5)(x- 12)

C.(x+3)(x-20) D.(x-5)(x+ 12)

1 1. Factorization 3x2-2xy-8y2 is obtained.

[ ]

A.(3x+4)(x-2) B.(3x-4)(x+2)

C.(3x+4y)(x-2y) D.(3x-4y)(x+2y)

12. Factorizing A2+8ab-33b2 to obtain

[ ]

A.(a+ 1 1)(a-3)b .(a- 1 1b)(a-3b)

C.(a+ 1 1b)(a-3b)d .(a- 1 1b)(a+3b)

13. factorize X4-3x2+2 to get.

[ ]

A.(x2-2)(x2- 1)b .(x2-2)(x+ 1)(x- 1)

C.(x2+2)(x2+ 1)d .(x2+2)(x+ 1)(x- 1)

14. the decomposable factor of polynomial x2-ax-bx+ab is

[ ]

A.-(x+a)(x+b) B.(x-a)(x+b)

C.(x-a)(x-b) D.(x+a)(x+b)

15. For a quadratic trinomial of X, the coefficient of the x2 term is 1, and the constant term is-12, which can decompose the factors. Such a quadratic trinomial is

[ ]

A.x2-11x-12 or x2+112.

B.x2-x- 12 or x2+x- 12

C x2-4x- 12 or x2+4x- 12

D. All the above can be done.

16. Exclude the following x3-x2-x+ 1, x2+y-xy-x, x2-2x-y2+ 1, (x2+3x) 2-(2x+ 1) 2.

[ ]

A. 1

C.3 D.4

The factorization factor of17.9-x2+12xy-36y2 is

[ ]

A.(x-6y+3)(x-6x-3)

B.-(x-6y+3)(x-6y-3)

C.-(x-6y+3)(x+6y-3)

D.-(x-6y+3)(x-6y+3)

18. The following factorization error is

[ ]

A.a2-bc+ac-ab=(a-b)(a+c)

B.ab-5a+3b- 15=(b-5)(a+3)

C.x2+3xy-2x-6y=(x+3y)(x-2)

d . x2-6xy- 1+9 y2 =(x+3y+ 1)(x+3y- 1)

19. It is known that A2X2 2x+B2 is completely flat, and both A and B are not zero, so the relationship between A and B is

[ ]

A. reciprocal or negative reciprocal

C. Equal number D. Arbitrary rational number

20. Decomposition of X4+4, the correct conclusion is

[ ]

A. factor B. There is a factor x2+2x+2.

C.(xy+2)(xy-8) D.(xy-2)(xy-8)

The factorization factor of 2 1.A4+2A2 B2+B4-A2B 2 is

[ ]

A.(a2+B2+ab)2b .(a2+B2+ab)(a2+B2-ab)

C.(a2-B2+ab)(a2-B2-ab)d .(a2+B2-ab)2

22.-(3x- 1) (x+2y) is the decomposition result of which of the following polynomials?

[ ]

A.3x2+6xy-x-2y B.3x2-6xy+x-2y

C.x+2y+3x2+6xy D.x+2y-3x2-6xy

23.64a8-B2 factorization is as follows

[ ]

A.(64 a4-b)(a4+b)b .( 16 a2-b)(4a 2+b)

C.(8a4-b)(8a4+b) D.(8a2-b)(8a4+b)

24.9 the factorization of (x-y) 2+12 (x2-y2)+4 (x+y) 2 is as follows

[ ]

A.(5x-y)2 B.(5x+y)2

C.(3x-2y)(3x+2y) D.(5x-2y)2

25.(2y-3x) 2-2 (3x-2y)+ 1 factorization is

[ ]

A.(3x-2y- 1)2 b .(3x+2y+ 1)2

C.(3x-2y+ 1)2d .(2y-3x- 1)2

26. the factorization of (a+b) 2-4 (a2-B2)+4 (a-b) 2 is as follows

[ ]

A.(3a-b)2 B.(3b+a)2

C.(3b-a)2 D.(3a+b)2

27. the decomposition factor of a2 (b+c) 2-2ab (a-c) (b+c)+B2 (a-c) 2 is

[ ]

Communication (a+b)2

C.c2(a+b)2 D.c2(a-b)

28. If the factor of 4xy-4x2-y2-k is (1-2x+y), the value of k is

[ ]

A.0 B. 1

C.- 1 D.4

29. The factorization factor 3a2x-4b2y-3b2x+4a2y is correct.

[ ]

A.-(a2+B2)(3x+4y)b .(a-b)(a+b)(3x+4y)

C.(a2+B2)(3x-4y)d .(a-b)(a+b)(3x-4y)

30. The factorization factor 2a2+4ab+2b2-8c2 is correct.

[ ]

A.2(a+b-2c) B.2(a+b+c)(a+b-c)

C.(2a+b+4c)(2a+b-4c)d . 2(a+b+2c)(a+b-2c)

Third, factorization:

1 . m2(p-q)-p+q；

2 . a(a b+ BC+AC)-ABC；

3 . x4-2y 4-2x3y+xy3；

4 . ABC(a2+B2+C2)-a3bc+2 ab2c 2；

5 . a2(b-c)+B2(c-a)+C2(a-b)；

6.(x2-2x)2+2x(x-2)+ 1；

7.(x-y)2+ 12(y-x)z+36z 2；

8 . x2-4ax+8ab-4 B2；

9.(ax+by)2+(ay-bx)2+2(ax+by)(ay-bx)；

10.( 1-a2)( 1-B2)-(a2- 1)2(B2- 1)2；

1 1.(x+ 1)2-9(x- 1)2；

12.4 a2 B2-(a2+B2-C2)2；

13 . ab2-ac2+4ac-4a；

14 . x3n+y3n；

15.(x+y)3+ 125；

16.(3m-2n)3+(3m+2n)3；

17 . X6(x2-y2)+y6(y2-x2)；

18.8(x+y)3+ 1；

19.(a+b+c)3-a3-B3-C3；

20 . x2+4xy+3 y2；

2 1 . x2+ 18x- 144；

22 . x4+2 x2-8；

23.-M4+ 18 m2- 17；

24 . X5-2x 3-8x；

25 . x8+ 19x 5-2 16x 2；

26.(x2-7x)2+ 10(x2-7x)-24；

27.5+7(a+ 1)-6(a+ 1)2；

28.(x2+x)(x2+x- 1)-2；

29 . x2+y2-x2 y2-4xy- 1；

30.(x- 1)(x-2)(x-3)(x-4)-48；

3 1 . x2-y2-x-y；

32 . ax2-bx2-bx+ax-3a+3b；

33 . M4+m2+ 1；

34 . a2-B2+2ac+C2；

35 . a3-ab2+a-b；

36.625 B4-(a-b)4；

37 . X6-y6+3x2y 4-3x4y 2；

38 . x2+4xy+4 y2-2x-4y-35；

39 . m2-a2+4ab-4b 2；

40.5m -5n-m2+2mn-n2.

IV. Proof (evaluation):

1. Given a+b = 0, find the value of a3-2b3+a2b-2ab2.

2. Prove that the product of four consecutive natural numbers plus 1 must be a complete square number.

3. Proof: (AC-BD) 2+(BC+AD) 2 = (A2+B2) (C2+D2).

4. Given a = k+3, b = 2k+2 and c = 3k- 1, find the value of a2+b2+c2+2ab-2bc-2ac.

5. If x2+MX+n = (x-3) (x+4), find the value of (m+n) 2.

6. When a is a value, the polynomial x2+7xy+AY2-5x+43y-24 can be decomposed into the product of two linear factors.

7. If x and y are arbitrary rational numbers, compare the sizes of 6xy and x2+9y2.

8. The square difference between two consecutive even numbers is a multiple of 4.

Reference answer:

First, fill in the blanks:

7.9，(3a- 1)

10.x-5y，x-5y，x-5y，2a-b

1 1.+5,-2

12.- 1, 2 (or -2, 1)

14.bc+ac，a+b，a-c

15.8 or -2

Second, multiple-choice questions:

1.B 2。 C 3。 C 4 explosive B 5。 B 6。 D 7。 An eight. C 9。 D 10。 B 1 1。 C 12。 C 13。 B 14。 C 15。 D 16。 B 17。 B 18。 D 19。 A 20. B 2 1。 B 22。 D 23。 C 24。 A handful of 25. A 26. C 27。 C 28。 C 29。 D 30。 D

Third, factorization:

1.(p-q)(m- 1)(m+ 1)。

8.(x-2b)(x-4a+2b)。

1 1.4(2x- 1)(2-x)。

20.(x+3y)(x+y)。

2 1.(x-6)(x+24)。

27.(3+2a)(2-3a)。

3 1.(x+y)(x-y- 1)。

38.(x+2y-7)(x+2y+5)。

IV. Proof (evaluation):

2. Hint: Let four consecutive natural numbers be n, n+ 1, n+2 and n+3.

6. Prompt: A =- 18.