初二数学计算题 初二下册数学计算题及答案100道

\u521d\u4e8c\u6570\u5b66\u8ba1\u7b97\u9898\u3002

\u24605\u221a8-2\u221a32+\u221a50
=5*3\u221a2-2*4\u221a2+5\u221a2
=\u221a2(15-8+5)
=12\u221a2
\u2461\u221a6-\u221a3/2-\u221a2/3
=\u221a6-\u221a6/2-\u221a6/3
=\u221a6/6
\u2462(\u221a45+\u221a27)-(\u221a4/3+\u221a125)
=(3\u221a5+3\u221a3)-(2\u221a3/3+5\u221a5)
=-2\u221a5+7\u221a5/3
\u2463(\u221a4a-\u221a50b)-2(\u221ab/2+\u221a9a)
=(2\u221aa-5\u221a2b)-2(\u221a2b/2+3\u221aa)
=-4\u221aa-6\u221a2b
\u2464\u221a4x*(\u221a3x/2-\u221ax/6)
=2\u221ax(\u221a6x/2-\u221a6x/6)
=2\u221ax*(\u221a6x/3)
=2/3*|x|*\u221a6
\u2465(x\u221ay-y\u221ax)\u00f7\u221axy
=x\u221ay\u00f7\u221axy-y\u221ax\u00f7\u221axy
=\u221ax-\u221ay
\u2466(3\u221a7+2\u221a3)(2\u221a3-3\u221a7)
=(2\u221a3)^2-(3\u221a7)^2
=12-63
=-51
\u2467(\u221a32-3\u221a3)(4\u221a2+\u221a27)
=(4\u221a2-3\u221a3)(4\u221a2+3\u221a3)
=(4\u221a2)^2-(3\u221a3)^2
=32-27
=5
\u2468(3\u221a6-\u221a4)?
=(3\u221a6)^2-2*3\u221a6*\u221a4+(\u221a4)^2
=54-12\u221a6+4
=58-12\u221a6
\u2469\uff081+\u221a2-\u221a3\uff09\uff081-\u221a2+\u221a3\uff09
=[1+(\u221a2-\u221a3)][1-(\u221a2-\u221a3)]
=1-(\u221a2-\u221a3)^2
=1-(2+3+2\u221a6)
=-4-2\u221a6
\uff081\uff095\u221a12\u00d7\u221a18
=5*2\u221a3*3\u221a2
=30\u221a6;
\uff082\uff09-6\u221a45\u00d7\uff08-4\u221a48\uff09
=6*3\u221a5*4*4\u221a3
=288\u221a15;
\uff083\uff09\u221a(12a)\u00d7\u221a(3a) /4
=\u221a(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)
\u6709\u7406\u6570\u7ec3\u4e60
\u7ec3\u4e60\u4e00(B\u7ea7)
(\u4e00)\u8ba1\u7b97\u9898:
(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+101*11*(101-92)
3.(23/4-3/4)*(3*6+2)
4. 3/7 \u00d7 49/9 - 4/3
5. 8/9 \u00d7 15/36 + 1/27
6. 12\u00d7 5/6 \u2013 2/9 \u00d73
7. 8\u00d7 5/4 + 1/4
8. 6\u00f7 3/8 \u2013 3/8 \u00f76
9. 4/7 \u00d7 5/9 + 3/7 \u00d7 5/9
10. 5/2 -\uff08 3/2 + 4/5 \uff09
11. 7/8 + \uff08 1/8 + 1/9 \uff09
12. 9 \u00d7 5/6 + 5/6
13. 3/4 \u00d7 8/9 - 1/3
14. 7 \u00d7 5/49 + 3/14
15. 6 \u00d7\uff08 1/2 + 2/3 \uff09
16. 8 \u00d7 4/5 + 8 \u00d7 11/5
17. 31 \u00d7 5/6 \u2013 5/6
18. 9/7 - \uff08 2/7 \u2013 10/21 \uff09
19. 5/9 \u00d7 18 \u2013 14 \u00d7 2/7
20. 4/5 \u00d7 25/16 + 2/3 \u00d7 3/4
21. 14 \u00d7 8/7 \u2013 5/6 \u00d7 12/15
22. 17/32 \u2013 3/4 \u00d7 9/24
23. 3 \u00d7 2/9 + 1/3
24. 5/7 \u00d7 3/25 + 3/7
25. 3/14 \u00d7\u00d7 2/3 + 1/6
26. 1/5 \u00d7 2/3 + 5/6
27. 9/22 + 1/11 \u00f7 1/2
28. 5/3 \u00d7 11/5 + 4/3
29. 45 \u00d7 2/3 + 1/3 \u00d7 15
30. 7/19 + 12/19 \u00d7 5/6
31. 1/4 + 3/4 \u00f7 2/3
32. 8/7 \u00d7 21/16 + 1/2
33. 101 \u00d7 1/5 \u2013 1/5 \u00d7 21
34.50\uff0b160\u00f740
35.120-144\u00f718+35
36.347+45\u00d72-4160\u00f752
37\uff0858+37\uff09\u00f7\uff0864-9\u00d75\uff09
38.95\u00f7\uff0864-45\uff09
39.178-145\u00f75\u00d76+42
40.812-700\u00f7\uff089+31\u00d711\uff09
41.85+14\u00d7\uff0814+208\u00f726\uff09
43.120-36\u00d74\u00f718+35
44.\uff0858+37\uff09\u00f7\uff0864-9\u00d75\uff09
45.(6.8-6.8\u00d70.55)\u00f78.5
46.0.12\u00d7 4.8\u00f70.12\u00d74.8
47.\uff083.2\u00d71.5+2.5\uff09\u00f71.6
48.6-1.6\u00f74= 5.38+7.85-5.37=
49.7.2\u00f70.8-1.2\u00d75= 6-1.19\u00d73-0.43=
50.6.5\u00d7\uff084.8-1.2\u00d74\uff09=
51.5.8\u00d7\uff083.87-0.13\uff09+4.2\u00d73.74
52.32.52-\uff086+9.728\u00f73.2\uff09\u00d72.5
53.[\uff087.1-5.6\uff09\u00d70.9-1.15] \u00f72.5
54.5.4\u00f7[2.6\u00d7\uff083.7-2.9\uff09+0.62]
55.12\u00d76\u00f7\uff0812-7.2\uff09-6
56.12\u00d76\u00f77.2-6
57.0.68\u00d71.9+0.32\u00d71.9
58.58+370\uff09\u00f7\uff0864-45\uff09
59.420+580-64\u00d721\u00f728
60.136+6\u00d7\uff0865-345\u00f723\uff09
15-10.75\u00d70.4-5.7
62.18.1\uff0b\uff083\uff0d0.299\u00f70.23\uff09\u00d71
63.(6.8-6.8\u00d70.55)\u00f78.5
64.0.12\u00d7 4.8\u00f70.12\u00d74.8
65.\uff083.2\u00d71.5+2.5\uff09\u00f71.6
66.3.2\u00d76+\uff081.5+2.5\uff09\u00f71.6
67.0.68\u00d71.9+0.32\u00d71.9
68.10.15-10.75\u00d70.4-5.7
69.5.8\u00d7\uff083.87-0.13\uff09+4.2\u00d73.74
70.32.52-\uff086+9.728\u00f73.2\uff09\u00d72.5
71.[\uff087.1-5.6\uff09\u00d70.9-1.15] \u00f72.5
72.5.4\u00f7[2.6\u00d7\uff083.7-2.9\uff09+0.62]
73.12\u00d76\u00f7\uff0812-7.2\uff09-6
74.12\u00d76\u00f77.2-6
75.33.02\uff0d\uff08148.4\uff0d90.85\uff09\u00f72.5
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+2/21
80./15*3/5
81.3/4/9/10-1/6
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 \u00d7 49/9 - 4/3
4) 9 \u00d7 15/36 + 1/27
5) 2\u00d7 5/6 \u2013 2/9 \u00d73
6) 3\u00d7 5/4 + 1/4
7) 94\u00f7 3/8 \u2013 3/8 \u00f76
8) 95/7 \u00d7 5/9 + 3/7 \u00d7 5/9
9) 6/2 -\uff08 3/2 + 4/5 \uff09
10) 8 + \uff08 1/8 + 1/9 \uff09
11) 8 \u00d7 5/6 + 5/6
12) 1/4 \u00d7 8/9 - 1/3
13) 10 \u00d7 5/49 + 3/14
14) 1.5 \u00d7\uff08 1/2 + 2/3 \uff09
15) 2\uff0f9 \u00d7 4/5 + 8 \u00d7 11/5
16) 3.1 \u00d7 5/6 \u2013 5/6
17) 4/7 - \uff08 2/7 \u2013 10/21 \uff09
18) 19 \u00d7 18 \u2013 14 \u00d7 2/7
19) 5 \u00d7 25/16 + 2/3 \u00d7 3/4
20) 4 \u00d7 8/7 \u2013 5/6 \u00d7 12/15
21) 7/32 \u2013 3/4 \u00d7 9/24
22) 1\u3001 2/3\u00f71/2\uff0d1/4\u00d72/5
2\u3001 2\uff0d6/13\u00f79/26\uff0d2/3
3\u3001 2/9\uff0b1/2\u00f74/5\uff0b3/8
4\u3001 10\u00f75/9\uff0b1/6\u00d74
5\u3001 1/2\u00d72/5\uff0b9/10\u00f79/20
6\u3001 5/9\u00d73/10\uff0b2/7\u00f72/5
7\u3001 1/2\uff0b1/4\u00d74/5\uff0d1/8
8\u3001 3/4\u00d75/7\u00d74/3\uff0d1/2
9\u3001 23\uff0d8/9\u00d71/27\u00f71/27
10\u3001 8\u00d75/6\uff0b2/5\u00f74
11\u3001 1/2\uff0b3/4\u00d75/12\u00d74/5
12\u3001 8/9\u00d73/4\uff0d3/8\u00f73/4
13\u3001 5/8\u00f75/4\uff0b3/23\u00f79/11
23) 1.2\u00d72.5+0.8\u00d72.5
24) 8.9\u00d71.25-0.9\u00d71.25
25) 12.5\u00d77.4\u00d70.8
26) 9.9\u00d76.4-\uff082.5+0.24\uff09\uff0827\uff09 6.5\u00d79.5+6.5\u00d70.5
0.35\u00d71.6+0.35\u00d73.4
0.25\u00d78.6\u00d74
6.72-3.28-1.72
0.45+6.37+4.55
5.4+6.9\u00d73-\uff0825-2.5\uff092\u00d741846-620-380
4.8\u00d746+4.8\u00d754
0.8+0.8\u00d72.5
1.25\u00d73.6\u00d78\u00d72.5-12.5\u00d72.4
28\u00d712.5-12.5\u00d720
23.65-\uff083.07+3.65\uff09
\uff084+0.4\u00d70.25\uff098\u00d77\u00d71.25
1.65\u00d799+1.65
27.85-\uff087.85+3.4\uff09
48\u00d71.25+50\u00d71.25\u00d70.2\u00d78
7.8\u00d79.9+0.78
(1010+309+4+681+6\uff09\u00d712
3\u00d79146\u00d7782\u00d76\u00d7854
5.15\u00d77/8+6.1-0.60625
1. 3/7 \u00d7 49/9 - 4/3
2. 8/9 \u00d7 15/36 + 1/27
3. 12\u00d7 5/6 \u2013 2/9 \u00d73
4. 8\u00d7 5/4 + 1/4
5. 6\u00f7 3/8 \u2013 3/8 \u00f76
6. 4/7 \u00d7 5/9 + 3/7 \u00d7 5/9
7. 5/2 -\uff08 3/2 + 4/5 \uff09
8. 7/8 + \uff08 1/8 + 1/9 \uff09
9. 9 \u00d7 5/6 + 5/6
10. 3/4 \u00d7 8/9 - 1/3
11. 7 \u00d7 5/49 + 3/14
12. 6 \u00d7\uff08 1/2 + 2/3 \uff09
13. 8 \u00d7 4/5 + 8 \u00d7 11/5
14. 31 \u00d7 5/6 \u2013 5/6
15. 9/7 - \uff08 2/7 \u2013 10/21 \uff09
16. 5/9 \u00d7 18 \u2013 14 \u00d7 2/7
17. 4/5 \u00d7 25/16 + 2/3 \u00d7 3/4
18. 14 \u00d7 8/7 \u2013 5/6 \u00d7 12/15
19. 17/32 \u2013 3/4 \u00d7 9/24
20. 3 \u00d7 2/9 + 1/3
21. 5/7 \u00d7 3/25 + 3/7
22. 3/14 \u00d7\u00d7 2/3 + 1/6
23. 1/5 \u00d7 2/3 + 5/6
24. 9/22 + 1/11 \u00f7 1/2
25. 5/3 \u00d7 11/5 + 4/3
26. 45 \u00d7 2/3 + 1/3 \u00d7 15
27. 7/19 + 12/19 \u00d7 5/6
28. 1/4 + 3/4 \u00f7 2/3
29. 8/7 \u00d7 21/16 + 1/2
30. 101 \u00d7 1/5 \u2013 1/5 \u00d7 21
31.50\uff0b160\u00f740 \uff0858+370\uff09\u00f7\uff0864-45\uff09
32.120-144\u00f718+35
33.347+45\u00d72-4160\u00f752
34\uff0858+37\uff09\u00f7\uff0864-9\u00d75\uff09
35.95\u00f7\uff0864-45\uff09
36.178-145\u00f75\u00d76+42 420+580-64\u00d721\u00f728
37.812-700\u00f7\uff089+31\u00d711\uff09 \uff08136+64\uff09\u00d7\uff0865-345\u00f723\uff09
38.85+14\u00d7\uff0814+208\u00f726\uff09
39.\uff08284+16\uff09\u00d7\uff08512-8208\u00f718\uff09
40.120-36\u00d74\u00f718+35
41.\uff0858+37\uff09\u00f7\uff0864-9\u00d75\uff09
42.(6.8-6.8\u00d70.55)\u00f78.5
43.0.12\u00d7 4.8\u00f70.12\u00d74.8
44.\uff083.2\u00d71.5+2.5\uff09\u00f71.6 \uff082\uff093.2\u00d7\uff081.5+2.5\uff09\u00f71.6
45.6-1.6\u00f74= 5.38+7.85-5.37=
46.7.2\u00f70.8-1.2\u00d75= 6-1.19\u00d73-0.43=
47.6.5\u00d7\uff084.8-1.2\u00d74\uff09= 0.68\u00d71.9+0.32\u00d71.9
48.10.15-10.75\u00d70.4-5.7
49.5.8\u00d7\uff083.87-0.13\uff09+4.2\u00d73.74
50.32.52-\uff086+9.728\u00f73.2\uff09\u00d72.5
51.[\uff087.1-5.6\uff09\u00d70.9-1.15] \u00f72.5
52.5.4\u00f7[2.6\u00d7\uff083.7-2.9\uff09+0.62]
53.12\u00d76\u00f7\uff0812-7.2\uff09-6 \uff084\uff0912\u00d76\u00f77.2-6
102\u00d74.5
7.8\u00d76.9\uff0b2.2\u00d76.9
5.6\u00d70.25
8\u00d7\uff0820\uff0d1.25\uff09
1\uff09127+352+73+44 \uff082\uff0989+276+135+33
\uff081\uff0925+71+75+29 +88 \uff082\uff09243+89+111+57
9405-2940\u00f728\u00d721
920-1680\u00f740\u00f77
690+47\u00d752-398
148+3328\u00f764-75
360\u00d724\u00f732+730
2100-94+48\u00d754
51+\uff082304-2042\uff09\u00d723
4215+\uff084361-716\uff09\u00f781
\uff08247+18\uff09\u00d727\u00f725
36-720\u00f7\uff08360\u00f718\uff09
1080\u00f7\uff0863-54\uff09\u00d780
\uff08528+912\uff09\u00d75-6178
8528\u00f741\u00d738-904
264+318-8280\u00f769
\uff08174+209\uff09\u00d726- 9000
814-\uff08278+322\uff09\u00f715
1406+735\u00d79\u00f745
3168-7828\u00f738+504
796-5040\u00f7\uff08630\u00f77\uff09
285+\uff083000-372\uff09\u00f736
1+5/6-19/12
3x(-9)+7x(-9
(-54)x1/6x(-1/3)
1.18.1\uff0b\uff083\uff0d0.299\u00f70.23\uff09\u00d71
2.(6.8-6.8\u00d70.55)\u00f78.5
3.0.12\u00d7 4.8\u00f70.12\u00d74.8
4.\uff083.2\u00d71.5+2.5\uff09\u00f71.6 \uff082\uff093.2\u00d7\uff081.5+2.5\uff09\u00f71.6
5.6-1.6\u00f74= 5.38+7.85-5.37=
6.7.2\u00f70.8-1.2\u00d75= 6-1.19\u00d73-0.43=
7.6.5\u00d7\uff084.8-1.2\u00d74\uff09= 0.68\u00d71.9+0.32\u00d71.9
8.10.15-10.75\u00d70.4-5.7
9.5.8\u00d7\uff083.87-0.13\uff09+4.2\u00d73.74
10.32.52-\uff086+9.728\u00f73.2\uff09\u00d72.5
11.[\uff087.1-5.6\uff09\u00d70.9-1.15] \u00f72.5
12.5.4\u00f7[2.6\u00d7\uff083.7-2.9\uff09+0.62]
13.12\u00d76\u00f7\uff0812-7.2\uff09-6
14.12\u00d76\u00f77.2-6
15.33.02\uff0d\uff08148.4\uff0d90.85\uff09\u00f72.5
7\u00d7(5/21+9/714)
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)
\u5199\u5b8c\u4e00\u904d\u540e\u518d\u522b\u8fd9\u4e9b\u9898\u5199\u4e00\u904d\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u8001\u5e08\u4eec\u770b\u4f5c\u4e1a\u90fd\u662f\u4e00\u770b\u800c\u8fc7\u4e0d\u4f1a\u4e00\u4e2a\u4e00\u4e2a\u6279\u7684\u3002

(1) 66x+17y=3967
25x+y=1200
\u7b54\u6848\uff1ax=48 y=47
(2) 18x+23y=2303
74x-y=1998
\u7b54\u6848\uff1ax=27 y=79
(3) 44x+90y=7796
44x+y=3476
\u7b54\u6848\uff1ax=79 y=48
(4) 76x-66y=4082
30x-y=2940
\u7b54\u6848\uff1ax=98 y=51
(5) 67x+54y=8546
71x-y=5680
\u7b54\u6848\uff1ax=80 y=59
(6) 42x-95y=-1410
21x-y=1575
\u7b54\u6848\uff1ax=75 y=48

\u5b9a\u4e49
\u52a0\u6cd5\uff1a\u628a\u4e24\u4e2a\u6570\u5408\u5e76\u6210\u4e00\u4e2a\u6570\u7684\u8fd0\u7b97\u3002
\u51cf\u6cd5\uff1a\u5728\u5df2\u77e5\u4e24\u4e2a\u52a0\u6570\u7684\u548c\u4e0e\u5176\u4e2d\u7684\u4e00\u4e2a\u52a0\u6570\uff0c\u6c42\u53e6\u4e00\u4e2a\u52a0\u6570\u7684\u8fd0\u7b97\u3002
\u4e58\u6cd5\uff1a\u6c42\u4e24\u4e2a\u6570\u4e58\u79ef\u7684\u8fd0\u7b97\u3002
\u4e00\u4e2a\u6570\u4e58\u6574\u6570\uff0c\u662f\u6c42\u51e0\u4e2a\u76f8\u540c\u52a0\u6570\u548c\u7684\u7b80\u4fbf\u8fd0\u7b97\u3002
\u9664\u6cd5\uff1a\u5df2\u77e5\u4e24\u4e2a\u56e0\u6570\u7684\u79ef\u4e0e\u5176\u4e2d\u7684\u4e00\u4e2a\u56e0\u6570\uff0c\u6c42\u53e6\u4e00\u4e2a\u56e0\u6570\u7684\u8fd0\u7b97\u3002
\u4ee5\u4e0a\u5185\u5bb9\u53c2\u8003\uff1a\u767e\u5ea6\u767e\u79d1-\u56db\u5219\u8fd0\u7b97

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
=-51
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)
有理数练习
练习一(B级)
(一)计算题:
(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+101*11*(101-92)
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 ）
11. 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 × 11/5
17. 31 × 5/6 – 5/6
18. 9/7 - （ 2/7 – 10/21 ）
19. 5/9 × 18 – 14 × 2/7
20. 4/5 × 25/16 + 2/3 × 3/4
21. 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 + 1/11 ÷ 1/2
28. 5/3 × 11/5 + 4/3
29. 45 × 2/3 + 1/3 × 15
30. 7/19 + 12/19 × 5/6
31. 1/4 + 3/4 ÷ 2/3
32. 8/7 × 21/16 + 1/2
33. 101 × 1/5 – 1/5 × 21
34.50＋160÷40
35.120-144÷18+35
36.347+45×2-4160÷52
37（58+37）÷（64-9×5）
38.95÷（64-45）
39.178-145÷5×6+42
40.812-700÷（9+31×11）
41.85+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）=
51.5.8×（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+580-64×21÷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
71.[（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+2/21
80./15*3/5
81.3/4/9/10-1/6
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 ）
11) 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 × 11/5
16) 3.1 × 5/6 – 5/6
17) 4/7 - （ 2/7 – 10/21 ）
18) 19 × 18 – 14 × 2/7
19) 5 × 25/16 + 2/3 × 3/4
20) 4 × 8/7 – 5/6 × 12/15
21) 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
11、 1/2＋3/4×5/12×4/5
12、 8/9×3/4－3/8÷3/4
13、 5/8÷5/4＋3/23÷9/11
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）2×41846-620-380
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
(1010+309+4+681+6）×12
3×9146×782×6×854
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
11. 7 × 5/49 + 3/14
12. 6 ×（ 1/2 + 2/3 ）
13. 8 × 4/5 + 8 × 11/5
14. 31 × 5/6 – 5/6
15. 9/7 - （ 2/7 – 10/21 ）
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
21. 5/7 × 3/25 + 3/7
22. 3/14 ×× 2/3 + 1/6
23. 1/5 × 2/3 + 5/6
24. 9/22 + 1/11 ÷ 1/2
25. 5/3 × 11/5 + 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 × 21/16 + 1/2
30. 101 × 1/5 – 1/5 × 21
31.50＋160÷40 （58+370）÷（64-45）
32.120-144÷18+35
33.347+45×2-4160÷52
34（58+37）÷（64-9×5）
35.95÷（64-45）
36.178-145÷5×6+42 420+580-64×21÷28
37.812-700÷（9+31×11） （136+64）×（65-345÷23）
38.85+14×（14+208÷26）
39.（284+16）×（512-8208÷18）
40.120-36×4÷18+35
41.（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
51.[（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+71+75+29 +88 （2）243+89+111+57
9405-2940÷28×21
920-1680÷40÷7
690+47×52-398
148+3328÷64-75
360×24÷32+730
2100-94+48×54
51+（2304-2042）×23
4215+（4361-716）÷81
（247+18）×27÷25
36-720÷（360÷18）
1080÷（63-54）×80
（528+912）×5-6178
8528÷41×38-904
264+318-8280÷69
（174+209）×26- 9000
814-（278+322）÷15
1406+735×9÷45
3168-7828÷38+504
796-5040÷（630÷7）
285+（3000-372）÷36
1+5/6-19/12
3x(-9)+7x(-9
(-54)x1/6x(-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
11.[（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×(5/21+9/714)
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)
写完一遍后再别这些题写一遍，以此类推，老师们看作业都是一看而过不会一个一个批的。

如图所示

鍒濅簩鏁板澶氶」寮忎箻澶氶」寮璁＄畻棰涓庝笉绛夊紡
绛旓細1銆(80+3)(80+7)=80*80+80*(3+7)+3*7=80*(80+10)=8*9*100+3*7 涓や釜鏁板瓧涓綅鏁颁箣鍜屼负10 瑙勫緥锛氫釜浣嶆暟鐩镐箻寰楀嚭鏈熬涓や釜鏁板瓧锛屽鏋滀箻绉负涓浣嶆暟锛屽湪鍓嶉潰娣0锛屽墿涓嬬殑鏁板瓧涔樹互锛堝畠鏈韩+1锛夊緱鍑虹殑缁撴灉鎺掑湪涓綅鏁扮浉涔樺緱鍑虹殑缁撴灉鐨勫墠闈 2銆3*4=12 5*5=25 35*35=1225 3銆49*锛49+...

鍒濅簩鏁板璁＄畻棰
绛旓細鍏堢畻绗竴閮ㄥ垎锛屽垎瀛愰儴鍒9鐨18娆℃柟鍙互鎷嗘垚锛3*3锛夌殑18娆℃柟锛屽垎瀛愬氨鎴愪簡锛3*3锛夌殑18娆℃柟-3鐨18娆℃柟锛屾彁涓3鐨18娆℃柟鍑烘潵锛屽緱鍒3鐨18娆℃柟涔樹互锛3鐨18娆℃柟-1锛夛紝鍒嗘瘝閮ㄥ垎6鐨18娆℃柟鍙互鎷嗘垚锛2*3锛夌殑18娆℃柟锛屽嵆2鐨18娆℃柟*3鐨18娆℃柟锛屽垎姣嶅氨鎴愪簡2鐨18娆℃柟*3鐨18娆℃柟-2鐨18娆℃柟锛屾彁涓2鐨18...

鍒濅簩鏁板瀹炴暟璁＄畻棰
绛旓細1.鑻ユ柟绋媥^2+px+q=0(p,q涓哄父鏁帮紝p^2-4q>0)鐨勪袱鏍逛负x1锛寈2锛屽垯x1+x2=___,x1*x2=___.2.宸茬煡鏂圭▼x^2-5x+3=0鐨勪袱涓牴涓簒1,x2锛璁＄畻涓嬪垪鍚勫紡鐨勫硷紙涓嶈В鏂圭▼锛(1)x1+x2;(2)x1*x2;(3)1/x1+1/x2;(4)x1^2+x2^2.闅忓爞浣滀笟鈥斿熀纭杈炬爣 1.濡傛灉鏂圭▼ax^2+bx+c=0(a=/...

鍒濅簩鏁板璁＄畻棰
绛旓細=2鈭2+9鈭2-3鈭2 =8鈭2 =鈭(3/2) x 鈭(4/5)=鈭(3/2 x 4/5)=鈭(6/5)=鈭30 /5 =(鈭16-2鈭2)/2+4鈭2 =2-鈭2+4鈭2 =2+3鈭2 =(鈭3)²-1 =3-1 =2 =3-2鈭6+2 =5-2鈭6 =(鈭5-2)^2004 * (鈭5+2)^(2004-1)=[(鈭5-2)(鈭5+2)]^2004/(...

鍒濅簩鏁板鍥犲紡鍒嗚В璁＄畻棰浜旈亾/
绛旓細鍥炵瓟锛1,=(a鈥揵)² a=m+n,b=2m 鎵浠=(n鈥搈)²

棰濇眰鍒濅簩鏁板璁＄畻棰,涓鐧句簲鍗佷釜
绛旓細棰濇眰鍒濅簩鏁板璁＄畻棰,涓鐧句簲鍗佷釜 瑕佷竴鐧句簲鍗佷釜鍒濅簩鍋氱殑璁＄畻棰橀璁颁綇浜嗘槸璁＄畻棰橀,鑰佸笀鍙垜浠仛鐨勯涓鍔犱竴绛変簬鍑犵殑棰橀兘鍙互浣嗘槸涓嶈澶... 瑕佷竴鐧句簲鍗佷釜鍒濅簩鍋氱殑璁＄畻棰橀璁颁綇浜嗘槸璁＄畻棰橀,鑰佸笀鍙垜浠仛鐨勯涓鍔犱竴绛変簬鍑犵殑棰橀兘鍙互浣嗘槸涓嶈澶 灞曞紑  鎴戞潵绛 ...

鍒濅簩鏁板澶氶」寮忎箻澶氶」寮璁＄畻棰涓庝笉绛夊紡
绛旓細鈶(2x-3)(x-4)-2(x-1)(2+3x)-(2x-5)(x+3)=31 - 10 x - 6 x^2 鈶★紙3x-2锛(2x+3)-6x(x-1)鈮2锛坸-2锛 9 x <= 2 x<=2/9 鈶紙2x-y)锛2x+y)+锛坸+y)锛坸-2y锛= 5 x^2 - x y - 3 y^2 鈶ｅ厛鍖栫畝锛屽啀姹傚硷紝(y-3)(4-5y+2y²)-2y(y&#...

涓閬鍒濅簩鏁板骞虫柟鏍璁＄畻棰銆
绛旓細瑙ｏ細鍘熷紡=3x+2=卤4 褰3x+2=-4鏃 瑙ｅ緱锛歺=-2 褰3x+2=4鏃 瑙ｅ緱锛歺=2/3 绛旓細x鐨勫兼槸-2鎴2/3.

鍒濅簩涓嬪唽鏁板璁＄畻棰銆
绛旓細鍥炵瓟锛(1)5/4ab (2) 0 (3)x=4

鎬ユ眰170閬鍒濅簩涓鏁板浠ｆ暟璁＄畻棰甯︾瓟妗 (鏁伴噺澶 涓瀹氳拷鍔)
绛旓細1) 66x+17y=3967 25x+y=1200 绛旀锛歺=48 y=47 (2) 18x+23y=2303 74x-y=1998 绛旀锛歺=27 y=79 (3) 44x+90y=7796 44x+y=3476 绛旀锛歺=79 y=48 (4) 76x-66y=4082 30x-y=2940 绛旀锛歺=98 y=51 (5) 67x+54y=8546 71x-y=5680 绛旀锛歺=80 y=59 (6) 42x-95y=...

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