=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.