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There is an answer to the math problem in grade two.
①5√8-2√32+√50

=5*3√2-2*4√2+5√2

=√2( 15-8+5)

= 12√2

②√6-√3/2-√2/3

=√6-√6/2-√6/3

=√6/6

③(√45+√27)-(√4/3+√ 125)

=(3√5+3√3)-(2√3/3+5√5)

=-2√5+7√5/3

④(√4a-√50b)-2(√b/2+√9a)

=(2√a-5√2b)-2(√2b/2+3√a)

=-4√a-6√2b

⑤√4x*(√3x/2-√x/6)

=2√x(√6x/2-√6x/6)

=2√x*(√6x/3)

=2/3*|x|*√6

⑥(x√y-y√x)÷√xy

=x√y÷√xy-y√x÷√xy

=√x-√y

⑦(3√7+2√3)(2√3-3√7)

=(2√3)^2-(3√7)^2

= 12-63

=-5 1

⑧(√32-3√3)(4√2+√27)

=(4√2-3√3)(4√2+3√3)

=(4√2)^2-(3√3)^2

=32-27

=5

⑨(3√6-√4)?

=(3√6)^2-2*3√6*√4+(√4)^2

=54- 12√6+4

=58- 12√6

⑩( 1+√2-√3)( 1-√2+√3)

=[ 1+(√2-√3)][ 1-(√2-√3)]

= 1-(√2-√3)^2

= 1-(2+3+2√6)

=-4-2√6

( 1)5√ 12×√ 18

=5*2√3*3√2

=30√6;

(2)-6√45×(-4√48)

=6*3√5*4*4√3

=288√ 15;

(3)√( 12a)×√(3a) /4

=√(36a^2)/4

=6a/4

=3a/2。

5.

x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2

=[x(y+z)-y(x-z)]^2

=(xz+yz)^2

=z^2(x+y)^2

6.

3(a+2)^2+28(a+2)-20

=[3(a+2)-2][(a+2)+ 10]

=(3a+4)(a+ 12)

7.

(a+b)^2-(b-c)^2+a^2-c^2

=(a+b)^2-c^2+a^2-(b-c)^2

=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)

=(a+b-c)(a+b+c+a-b+c)

=2(a+b-c)(a+c)

8.

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

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

=(x^2+x)^2-(x^2+x)-2

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

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

9.

9x^2(x- 1)^2-3(x^2-x)-56

=9x^2(x- 1)^2-3x(x- 1)-56

=[3x(x- 1)-8][3x(x- 1)+7]

=(3x^2-3x-8)(3x^2-3x+7)

Rational number exercise

Exercise1(level b)

(1) Calculation problem:

( 1)23+(-73) (2)(-84)+(-49) (3)7+(-2.04) (4)4.23+(-7.57) (5)(-7/3)+(-7/6) (6)9/4+(-3/2) (7)3.75+(2.25)+5/4 (8)-3.75+(+5/4)+(- 1.5)

5.

x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2

=[x(y+z)-y(x-z)]^2

=(xz+yz)^2

=z^2(x+y)^2

6.

3(a+2)^2+28(a+2)-20

=[3(a+2)-2][(a+2)+ 10]

=(3a+4)(a+ 12)

7.

(a+b)^2-(b-c)^2+a^2-c^2

=(a+b)^2-c^2+a^2-(b-c)^2

=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)

=(a+b-c)(a+b+c+a-b+c)

=2(a+b-c)(a+c)

8.

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

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

=(x^2+x)^2-(x^2+x)-2

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

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

9.

9x^2(x- 1)^2-3(x^2-x)-56

=9x^2(x- 1)^2-3x(x- 1)-56

=[3x(x- 1)-8][3x(x- 1)+7]

=(3x^2-3x-8)(3x^2-3x+7)

1. 125*3+ 125*5+25*3+25

2.9999*3+ 10 1* 1 1*( 10 1-92)

3.(23/4-3/4)*(3*6+2)

4.3/7 × 49/9 - 4/3

5.8/9 × 15/36 + 1/27

6. 12× 5/6 – 2/9 ×3

7.8× 5/4 + 1/4

8.6÷ 3/8 – 3/8 ÷6

9.4/7 × 5/9 + 3/7 × 5/9

10.5/2 -( 3/2 + 4/5 )

1 1.7/8 + ( 1/8 + 1/9 )

12.9 × 5/6 + 5/6

13.3/4 × 8/9 - 1/3

14.7 × 5/49 + 3/ 14

15.6 ×( 1/2 + 2/3 )

16.8 × 4/5 + 8 × 1 1/5

17.3 1 × 5/6 – 5/6

18.9/7 - ( 2/7 – 10/2 1 )

19.5/9 × 18 – 14 × 2/7

20.4/5 × 25/ 16 + 2/3 × 3/4

2 1. 14 × 8/7 – 5/6 × 12/ 15

22. 17/32 – 3/4 × 9/24

23.3 × 2/9 + 1/3

24.5/7 × 3/25 + 3/7

25.3/ 14 ×× 2/3 + 1/6

26. 1/5 × 2/3 + 5/6

27.9/22 + 1/ 1 1 ÷ 1/2

28.5/3 × 1 1/5 + 4/3

29.45 × 2/3 + 1/3 × 15

30.7/ 19 + 12/ 19 × 5/6

3 1. 1/4 + 3/4 ÷ 2/3

32.8/7 × 2 1/ 16 + 1/2

33. 10 1 × 1/5 – 1/5 × 2 1

34.50+ 160÷40

35. 120- 144÷ 18+35

36.347+45×2-4 160÷52

37(58+37)÷(64-9×5)

38.95÷(64-45)

39. 178- 145÷5×6+42

40.8 12-700÷(9+3 1× 1 1)

4 1.85+ 14×( 14+208÷26)

43. 120-36×4÷ 18+35

44.(58+37)÷(64-9×5)

45.(6.8-6.8×0.55)÷8.5

46.0. 12× 4.8÷0. 12×4.8

47.(3.2× 1.5+2.5)÷ 1.6

48.6- 1.6÷4= 5.38+7.85-5.37=

49.7.2÷0.8- 1.2×5= 6- 1. 19×3-0.43=

50.6.5×(4.8- 1.2×4)=

5 1.5.8×(3.87-0. 13)+4.2×3.74

52.32.52-(6+9.728÷3.2)×2.5

53.[(7. 1-5.6)×0.9- 1. 15] ÷2.5

54.5.4÷[2.6×(3.7-2.9)+0.62]

55. 12×6÷( 12-7.2)-6

56. 12×6÷7.2-6

57.0.68× 1.9+0.32× 1.9

58.58+370)÷(64-45)

59.420+580-64×2 1÷28

60. 136+6×(65-345÷23)

15- 10.75×0.4-5.7

62. 18. 1+(3-0.299÷0.23)× 1

63.(6.8-6.8×0.55)÷8.5

64.0. 12× 4.8÷0. 12×4.8

65.(3.2× 1.5+2.5)÷ 1.6

66.3.2×6+( 1.5+2.5)÷ 1.6

67.0.68× 1.9+0.32× 1.9

68. 10. 15- 10.75×0.4-5.7

69.5.8×(3.87-0. 13)+4.2×3.74

70.32.52-(6+9.728÷3.2)×2.5

7 1.[(7. 1-5.6)×0.9- 1. 15] ÷2.5

72.5.4÷[2.6×(3.7-2.9)+0.62]

73. 12×6÷( 12-7.2)-6

74. 12×6÷7.2-6

75.33.02-( 148.4-90.85)÷2.5

1) 76.(25%-695%- 12%)*36

77./4*3/5+3/4*2/5

78. 1- 1/4+8/9/7/9

79.+ 1/6/3/24+2/2 1

80./ 15*3/5

8 1.3/4/9/ 10- 1/6

82./3+ 1/2)/5/6- 1/3]/ 1/7

83./5+3/5/2+3/4

84.(2-2/3/ 1/2)]*2/5

85.+5268.32-2569

86.3+456-52*8

87.5%+6325

88./2+ 1/3+ 1/4

2) 89+456-78

3) 5%+.3/7 × 49/9 - 4/3

4) 9 × 15/36 + 1/27

5) 2× 5/6 – 2/9 ×3

6) 3× 5/4 + 1/4

7) 94÷ 3/8 – 3/8 ÷6

8) 95/7 × 5/9 + 3/7 × 5/9

9) 6/2 -( 3/2 + 4/5 )

10) 8 + ( 1/8 + 1/9 )

1 1) 8 × 5/6 + 5/6

12) 1/4 × 8/9 - 1/3

13) 10 × 5/49 + 3/ 14

14) 1.5 ×( 1/2 + 2/3 )

15) 2/9 × 4/5 + 8 × 1 1/5

16) 3. 1 × 5/6 – 5/6

17) 4/7 - ( 2/7 – 10/2 1 )

18) 19 × 18 – 14 × 2/7

19) 5 × 25/ 16 + 2/3 × 3/4

20) 4 × 8/7 – 5/6 × 12/ 15

2 1) 7/32 – 3/4 × 9/24

22) 1、 2/3÷ 1/2- 1/4×2/5

2、 2-6/ 13÷9/26-2/3

3、 2/9+ 1/2÷4/5+3/8

4、 10÷5/9+ 1/6×4

5、 1/2×2/5+9/ 10÷9/20

6、 5/9×3/ 10+2/7÷2/5

7、 1/2+ 1/4×4/5- 1/8

8、 3/4×5/7×4/3- 1/2

9、 23-8/9× 1/27÷ 1/27

10、 8×5/6+2/5÷4

1 1、 1/2+3/4×5/ 12×4/5

12、 8/9×3/4-3/8÷3/4

13、 5/8÷5/4+3/23÷9/ 1 1

23) 1.2×2.5+0.8×2.5

24) 8.9× 1.25-0.9× 1.25

25) 12.5×7.4×0.8

26) 9.9×6.4-(2.5+0.24)(27) 6.5×9.5+6.5×0.5

0.35× 1.6+0.35×3.4

0.25×8.6×4

6.72-3.28- 1.72

0.45+6.37+4.55

5.4+6.9×3-(25-2.5)2×4 1846-620-380

4.8×46+4.8×54

0.8+0.8×2.5

1.25×3.6×8×2.5- 12.5×2.4

28× 12.5- 12.5×20

23.65-(3.07+3.65)

(4+0.4×0.25)8×7× 1.25

1.65×99+ 1.65

27.85-(7.85+3.4)

48× 1.25+50× 1.25×0.2×8

7.8×9.9+0.78

( 10 10+309+4+68 1+6)× 12

3×9 146×782×6×854

5. 15×7/8+6. 1-0.60625

1.3/7 × 49/9 - 4/3

2.8/9 × 15/36 + 1/27

3. 12× 5/6 – 2/9 ×3

4.8× 5/4 + 1/4

5.6÷ 3/8 – 3/8 ÷6

6.4/7 × 5/9 + 3/7 × 5/9

7.5/2 -( 3/2 + 4/5 )

8.7/8 + ( 1/8 + 1/9 )

9.9 × 5/6 + 5/6

10.3/4 × 8/9 - 1/3

1 1.7 × 5/49 + 3/ 14

12.6 ×( 1/2 + 2/3 )

13.8 × 4/5 + 8 × 1 1/5

14.3 1 × 5/6 – 5/6

15.9/7 - ( 2/7 – 10/2 1 )

16.5/9 × 18 – 14 × 2/7

17.4/5 × 25/ 16 + 2/3 × 3/4

18. 14 × 8/7 – 5/6 × 12/ 15

19. 17/32 – 3/4 × 9/24

20.3 × 2/9 + 1/3

2 1.5/7 × 3/25 + 3/7

22.3/ 14 ×× 2/3 + 1/6

23. 1/5 × 2/3 + 5/6

24.9/22 + 1/ 1 1 ÷ 1/2

25.5/3 × 1 1/5 + 4/3

26.45 × 2/3 + 1/3 × 15

27.7/ 19 + 12/ 19 × 5/6

28. 1/4 + 3/4 ÷ 2/3

29.8/7 × 2 1/ 16 + 1/2

30. 10 1 × 1/5 – 1/5 × 2 1

3 1.50+ 160÷40 (58+370)÷(64-45)

32. 120- 144÷ 18+35

33.347+45×2-4 160÷52

34(58+37)÷(64-9×5)

35.95÷(64-45)

36. 178- 145÷5×6+42 420+580-64×2 1÷28

37.8 12-700÷(9+3 1× 1 1) ( 136+64)×(65-345÷23)

38.85+ 14×( 14+208÷26)

39.(284+ 16)×(5 12-8208÷ 18)

40. 120-36×4÷ 18+35

4 1.(58+37)÷(64-9×5)

42.(6.8-6.8×0.55)÷8.5

43.0. 12× 4.8÷0. 12×4.8

44.(3.2× 1.5+2.5)÷ 1.6 (2)3.2×( 1.5+2.5)÷ 1.6

45.6- 1.6÷4= 5.38+7.85-5.37=

46.7.2÷0.8- 1.2×5= 6- 1. 19×3-0.43=

47.6.5×(4.8- 1.2×4)= 0.68× 1.9+0.32× 1.9

48. 10. 15- 10.75×0.4-5.7

49.5.8×(3.87-0. 13)+4.2×3.74

50.32.52-(6+9.728÷3.2)×2.5

5 1.[(7. 1-5.6)×0.9- 1. 15] ÷2.5

52.5.4÷[2.6×(3.7-2.9)+0.62]

53. 12×6÷( 12-7.2)-6 (4) 12×6÷7.2-6

102×4.5

7.8×6.9+2.2×6.9

5.6×0.25

8×(20- 1.25)

1) 127+352+73+44 (2)89+276+ 135+33

( 1)25+7 1+75+29 +88 (2)243+89+ 1 1 1+57

9405-2940÷28×2 1

920- 1680÷40÷7

690+47×52-398

148+3328÷64-75

360×24÷32+730

2 100-94+48×54

5 1+(2304-2042)×23

42 15+(436 1-7 16)÷8 1

(247+ 18)×27÷25

36-720÷(360÷ 18)

1080÷(63-54)×80

(528+9 12)×5-6 178

8528÷4 1×38-904

264+3 18-8280÷69

( 174+209)×26- 9000

8 14-(278+322)÷ 15

1406+735×9÷45

3 168-7828÷38+504

796-5040÷(630÷7)

285+(3000-372)÷36

1+5/6- 19/ 12

3x(-9)+7x(-9

(-54)x 1/6x(- 1/3)

1. 18. 1+(3-0.299÷0.23)× 1

2.(6.8-6.8×0.55)÷8.5

3.0. 12× 4.8÷0. 12×4.8

4.(3.2× 1.5+2.5)÷ 1.6 (2)3.2×( 1.5+2.5)÷ 1.6

5.6- 1.6÷4= 5.38+7.85-5.37=

6.7.2÷0.8- 1.2×5= 6- 1. 19×3-0.43=

7.6.5×(4.8- 1.2×4)= 0.68× 1.9+0.32× 1.9

8. 10. 15- 10.75×0.4-5.7

9.5.8×(3.87-0. 13)+4.2×3.74

10.32.52-(6+9.728÷3.2)×2.5

1 1.[(7. 1-5.6)×0.9- 1. 15] ÷2.5

12.5.4÷[2.6×(3.7-2.9)+0.62]

13. 12×6÷( 12-7.2)-6

14. 12×6÷7.2-6

15.33.02-( 148.4-90.85)÷2.5

7×(5/2 1+9/7 14)

a^3-2b^3+ab(2a-b)

=a^3+2a^2b-2b^3-ab^2

=a^2(a+2b)-b^2(2b+a)

=(a+2b)(a^2-b^2)

=(a+2b)(a+b)(a-b)

2.

(x^2+y^2)^2-4y(x^2+y^2)+4y^2

=(x^2+y^2-2y)^2

3.

(x^2+2x)^2+3(x^2+2x)+x^2+2x+3

=(x^2+2x)^2+4(x^2+2x)+3

=(x^2+2x+3)(x^2+2x+ 1)

=(x^2+2x+3)(x+ 1)^2

4.

(a+ 1)(a+2)+(2a+ 1)(a-2)- 12

=a^2+3a+2+2a^2-3a-2- 12

=3a^2- 12

=3(a+2)(a-2)

5.

x^2(y+z)^2-2xy(x-z)(y+z)+y^2(x-z)^2

=[x(y+z)-y(x-z)]^2

=(xz+yz)^2

=z^2(x+y)^2

6.

3(a+2)^2+28(a+2)-20

=[3(a+2)-2][(a+2)+ 10]

=(3a+4)(a+ 12)

7.

(a+b)^2-(b-c)^2+a^2-c^2

=(a+b)^2-c^2+a^2-(b-c)^2

=(a+b+c)(a+b-c)+(a+b-c)(a-b+c)

=(a+b-c)(a+b+c+a-b+c)

=2(a+b-c)(a+c)

8.

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

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

=(x^2+x)^2-(x^2+x)-2

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

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

Don't write these questions after you finish them, and so on. Teachers don't approve homework one by one when they look at it.