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EASY MULTIPLICATION

EASY MULTIPLICATION:
By using formula (a+b)(a-b)=a2-b2    we can do  easy multiplication.
In this case we are using base numbers as 100,400,900,1600,2500,3600,4900,6400,8100,10000.
We need to practice the the square numbers from 12  to atleast 502.
Base number:10
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of base number (100).In fourth column we are subtracting squared numbers from a base number.
9x11
(10-1)(10+1)
(102-12)
(100-1)
99
8x12
(10-2)(10+2)
(102-22)
(100-4)
96
7x13
(10-3)(10+3)
(102-32)
(100-9)
91
6x14
(10-4)(10+4)
(102-42)
(100-16)
84
5x15
(10-5)(10+5)
(102-52)
(100-25)
75
4x16
(10-6)(10+6)
(102-62)
(100-36)
64
3x17
(10-7)(10+7)
(102-72)
(100-49)
51
2x18
(10-8)(10+8)
(102-82)
(100-64)
36
1x19
(10-9)(10+9)
(102-92)
(100-81)
19

Base number:20
By using formula  (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(400).In fourth column we are subtracting squared numbers from a square of base number.





19x21
(20-1)(20+1)
(202-12)
(400-1)
399
18x22
(20-2)(20+2)
(202-22)
(400-4)
396
17x23
(20-3)(20+3)
(202-32)
(400-9)
391
16x24
(20-4)(20+4)
(202-42)
(400-16)
384
15x25
(20-5)(20+5)
(202-52)
(400-25)
375
14x26
(20-6)(20+6)
(202-62)
(400-36)
364
13x27
(20-7)(20+7)
(202-72)
(400-49)
351
12x28
(20-8)(20+8)
(202-82)
(400-64)
336
11x29
(20-9)(20+9)
(202-92)
(400-81)
319
10x30
(20-10)(20+10)
(202-102)
(400-100)
300
9x31
(20-11)(20+11)
(202-112)
(400-121)
279
8x32
(20-12)(20+12)
(202-122)
(400-144)
256
7x33
(20-13)(20+13)
(202-132)
(400-169)
231
6x34
(20-14)(20+14)
(202-142)
(400-196)
204
5x35
(20-15)(20+15)
(202-152)
(400-225)
175
4x36
(20-16)(20+16)
(202-162)
(400-256)
144
3x37
(20-17)(20+17)
(202-172)
(400-289)
111
2x38
(20-18)(20+18)
(202-182)
(400-324)
76
1x39
(20-19)(20+19)
(202-192)
(400-361)
39


Base number:30
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(900).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.





29x31
(30-1)(30+1)
(302-12)
(900-1)
899
28x32
(30-2)(30+2)
(302-22)
(900-4)
896
27x33
(30-3)(30+3)
(302-32)
(900-9)
891
26x34
(30-4)(30+4)
(302-42)
(900-16)
884
25x35
(30-5)(30+5)
(302-52)
(900-25)
875
24x36
(30-6)(30+6)
(302-62)
(900-36)
864
23x37
(30-7)(30+7)
(302-72)
(900-49)
851
22x38
(30-8)(30+8)
(302-82)
(900-64)
836
21x39
(30-9)(30+9)
(302-92)
(900-81)
819
20x40
(30-10)(30+10)
(302-102)
(900-100)
800
19x41
(30-11)(30+11)
(302-112)
(900-121)
779
18x42
(30-12)(30+12)
(302-122)
(900-144)
756
17x43
(30-13)(30+13)
(302-132)
(900-169)
731
16x44
(30-14)(30+14)
(302-142)
(900-196)
704
15x45
(30-15)(30+15)
(302-152)
(900-225)
675
14x46
(30-16)(30+16)
(302-162)
(900-256)
644
13x47
(30-17)(30+17)
(302-172)
(900-289)
611
12x48
(30-18)(30+18)
(302-182)
(900-324)
576
11x49
(30-19)(30+19)
(302-192)
(900-361)
539
10x50
(30-20)(30+20)
(302-202)
(900-400)
500
9x51
(30-21)(30+21)
(302-212)
(900-441)
459
8x52
(30-22)(30+22)
(302-222)
(900-484)
416
7x53
(30-23)(30+23)
(302-232)
(900-529)
371
6x54
(30-24)(30+24)
(302-242)
(900-576)
324
5x55
(30-25)(30+25)
(302-252)
(900-625)
275
4x56
(30-26)(30+26)
(302-262)
(900-676)
224
3x57
(30-27)(30+27)
(302-272)
(900-729)
171
2x58
(30-28)(30+28)
(302-282)
(900-784)
116
1x59
(30-29)(30+29)
(302-292)
(900-841)
59

Base number:40
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(1600).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.
39x41
(40-1)(40+1)
(402-12)
(1600-1)
1599
38x42
(40-2)(40+2)
(402-22)
(1600-4)
1596
37x43
(40-3)(40+3)
(402-32)
(1600-9)
1591
36x44
(40-4)(40+4)
(402-42)
(1600-16)
1584
35x45
(40-5)(40+5)
(402-52)
(1600-25)
1575
34x46
(40-6)(40+6)
(402-62)
(1600-36)
1564
33x47
(40-7)(40+7)
(402-72)
(1600-49)
1551
32x48
(40-8)(40+8)
(402-82)
(1600-64)
1536
31x49
(40-9)(40+9)
(402-92)
(1600-81)
1519
30x50
(40-10)(40+10)
(402-102)
(1600-100)
1500
29x51
(40-11)(40+11)
(402-112)
(1600-121)
1479
28x52
(40-12)(40+12)
(402-122)
(1600-144)
1456
27x53
(40-13)(40+13)
(402-132)
(1600-169)
1431
26x54
(40-14)(40+14)
(402-142)
(1600-196)
1404
25x55
(40-15)(40+15)
(402-152)
(1600-225)
1375
24x56
(40-16)(40+16)
(402-162)
(1600-256)
1344
23x57
(40-17)(40+17)
(402-172)
(1600-289)
1311
22x58
(40-18)(40+18)
(402-182)
(1600-324)
1276
21x59
(40-19)(40+19)
(402-192)
(1600-361)
1239
20x60
(40-20)(40+20)
(402-202)
(1600-400)
1200
19x61
(40-21)(40+21)
(402-212)
(1600-441)
1159
18x62
(40-22)(40+22)
(402-222)
(1600-484)
1116
17x63
(40-23)(40+23)
(402-232)
(1600-529)
1071
16x64
(40-24)(40+24)
(402-242)
(1600-576)
1024
15x65
(40-25)(40+25)
(402-252)
(1600-625)
975
14x66
(40-26)(40+26)
(402-262)
(1600-676)
924
13x67
(40-27)(40+27)
(402-272)
(1600-729)
871
12x68
(40-28)(40+28)
(402-282)
(1600-784)
816
11x69
(40-29)(40+29)
(402-292)
(1600-841)
759
10x70
(40-30)(40+30)
(402-302)
(1600-900)
700
9x71
(40-31)(40+31)
(402-312)
(1600-961)
639
8x72
(40-32)(40+32)
(402-322)
(1600-1024)
576
7x73
(40-33)(40+33)
(402-332)
(1600-1089)
511
6x74
(40-34)(40+34)
(402-342)
(1600-1156)
444
5x75
(40-35)(40+35)
(402-352)
(1600-1225)
375
4x76
(40-36)(40+36)
(402-362)
(1600-1296)
304
3x77
(40-37)(40+37)
(402-372)
(1600-1369)
231
2x78
(40-38)(40+38)
(402-382)
(1600-1444)
156
1x79
(40-39)(40+39)
(402-392)
(1600-1521)
79

Base number:50
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(2500).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.


49x51
(50-1)(50+1)
(502-12)
(2500-1)
2499
48x52
(50-2)(50+2)
(502-22)
(2500-4)
2496
47x53
(50-3)(50+3)
(502-32)
(2500-9)
2491
46x54
(50-4)(50+4)
(502-42)
(2500-16)
2484
45x55
(50-5)(50+5)
(502-52)
(2500-25)
2475
44x56
(50-6)(50+6)
(502-62)
(2500-36)
2464
43x57
(50-7)(50+7)
(502-72)
(2500-49)
2451
42x58
(50-8)(50+8)
(502-82)
(2500-64)
2436
41x59
(50-9)(50+9)
(502-92)
(2500-81)
2419
40x60
(50-10)(50+10)
(502-102)
(2500-100)
2400
39x61
(50-11)(50+11)
(502-112)
(2500-121)
2379
38x62
(50-12)(50+12)
(502-122)
(2500-144)
2356
37x63
(50-13)(50+13)
(502-132)
(2500-169)
2331
36x64
(50-14)(50+14)
(502-142)
(2500-196)
2304
35x65
(50-15)(50+15)
(502-152)
(2500-225)
2275
34x66
(50-16)(50+16)
(502-162)
(2500-256)
2244
33x67
(50-17)(50+17)
(502-172)
(2500-289)
2211
32x68
(50-18)(50+18)
(502-182)
(2500-324)
2176
31x69
(50-19)(50+19)
(502-192)
(2500-361)
2139
30x70
(50-20)(50+20)
(502-202)
(2500-400)
2100
29x71
(50-21)(50+21)
(502-212)
(2500-441)
2059
28x72
(50-22)(50+22)
(502-222)
(2500-484)
2016
27x73
(50-23)(50+23)
(502-232)
(2500-529)
1971
26x74
(50-24)(50+24)
(502-242)
(2500-576)
1924
25x75
(50-25)(50+25)
(502-252)
(2500-625)
1875
24x76
(50-26)(50+26)
(502-262)
(2500-676)
1824
23x77
(50-27)(50+27)
(502-272)
(2500-729)
1771
22x78
(50-28)(50+28)
(502-282)
(2500-784)
1716
21x79
(50-29)(50+29)
(502-292)
(2500-841)
1659
20x80
(50-30)(50+30)
(502-302)
(2500-900)
1600
19x81
(50-31)(50+31)
(502-312)
(2500-961)
1539
18x82
(50-32)(50+32)
(502-322)
(2500-1024)
1476
17x83
(50-33)(50+33)
(502-332)
(2500-1089)
1411
16x84
(50-34)(50+34)
(502-342)
(2500-1156)
1344
15x85
(50-35)(50+35)
(502-352)
(2500-1225)
1275
14x86
(50-36)(50+36)
(502-362)
(2500-1296)
1204
13x87
(50-37)(50+37)
(502-372)
(2500-1369)
1131
12x88
(50-38)(50+38)
(502-382)
(2500-1444)
1056
11x89
(50-39)(50+39)
(502-392)
(2500-1521)
979


Base number:60
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(3600).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.
59x61
(60-1)(60+1)
(602-12)
(3600-1)
3599
58x62
(60-2)(60+2)
(602-22)
(3600-4)
3596
57x63
(60-3)(60+3)
(602-32)
(3600-9)
3591
56x64
(60-4)(60+4)
(602-42)
(3600-16)
3584
55x65
(60-5)(60+5)
(602-52)
(3600-25)
3575
54x66
(60-6)(60+6)
(602-62)
(3600-36)
3564
53x67
(60-7)(60+7)
(602-72)
(3600-49)
3551
52x68
(60-8)(60+8)
(602-82)
(3600-64)
3536
51x69
(60-9)(60+9)
(602-92)
(3600-81)
3519
50x70
(60-10)(60+10)
(602-102)
(3600-100)
3500
49x71
(60-11)(60+11)
(602-112)
(3600-121)
3479
48x72
(60-12)(60+12)
(602-122)
(3600-144)
3456
47x73
(60-13)(60+13)
(602-132)
(3600-169)
3431
46x74
(60-14)(60+14)
(602-142)
(3600-196)
3404
45x75
(60-15)(60+15)
(602-152)
(3600-225)
3375
44x76
(60-16)(60+16)
(602-162)
(3600-256)
3344
43x77
(60-17)(60+17)
(602-172)
(3600-289)
3311
42x78
(60-18)(60+18)
(602-182)
(3600-324)
3276
41x79
(60-19)(60+19)
(602-192)
(3600-361)
3239
40x80
(60-20)(60+20)
(602-202)
(3600-400)
3200
39x81
(60-21)(60+21)
(602-212)
(3600-441)
3159
38x82
(60-22)(60+22)
(602-222)
(3600-484)
3116
37x83
(60-23)(60+23)
(602-232)
(3600-529)
3071
36x84
(60-24)(60+24)
(602-242)
(3600-576)
3024
35x85
(60-25)(60+25)
(602-252)
(3600-625)
2975
34x86
(60-26)(60+26)
(602-262)
(3600-676)
2924
33x87
(60-27)(60+27)
(602-272)
(3600-729)
2871
32x88
(60-28)(60+28)
(602-282)
(3600-784)
2816
31x89
(60-29)(60+29)
(602-292)
(3600-841)
2759
30x90
(60-30)(60+30)
(602-302)
(3600-900)
2700
29x91
(60-31)(60+31)
(602-312)
(3600-961)
2639
28x92
(60-32)(60+32)
(602-322)
(3600-1024)
2576
27x93
(60-33)(60+33)
(602-332)
(3600-1089)
2511
26x94
(60-34)(60+34)
(602-342)
(3600-1156)
2444
25x95
(60-35)(60+35)
(602-352)
(3600-1225)
2375



Base number:70
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(4900).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.
69x71
(70-1)(70+1)
(702-12)
(4900-1)
4899
68x72
(70-2)(70+2)
(702-22)
(4900-4)
4896
67x73
(70-3)(70+3)
(702-32)
(4900-9)
4891
66x74
(70-4)(70+4)
(702-42)
(4900-16)
4884
65x75
(70-5)(70+5)
(702-52)
(4900-25)
4875
64x76
(70-6)(70+6)
(702-62)
(4900-36)
4864
63x77
(70-7)(70+7)
(702-72)
(4900-49)
4851
62x78
(70-8)(70+8)
(702-82)
(4900-64)
4836
61x79
(70-9)(70+9)
(702-92)
(4900-81)
4819
60x80
(70-10)(70+10)
(702-102)
(4900-100)
4800
59x81
(70-11)(70+11)
(702-112)
(4900-121)
4779
58x82
(70-12)(70+12)
(702-122)
(4900-144)
4756
57x83
(70-13)(70+13)
(702-132)
(4900-169)
4731
56x84
(70-14)(70+14)
(702-142)
(4900-196)
4704
55x85
(70-15)(70+15)
(702-152)
(4900-225)
4675
54x86
(70-16)(70+16)
(702-162)
(4900-256)
4644
53x87
(70-17)(70+17)
(702-172)
(4900-289)
4611
52x88
(70-18)(70+18)
(702-182)
(4900-324)
4576
51x89
(70-19)(70+19)
(702-192)
(4900-361)
4539
50x90
(70-20)(70+20)
(702-202)
(4900-400)
4500
49x91
(70-21)(70+21)
(702-212)
(4900-441)
4459
48x92
(70-22)(70+22)
(702-222)
(4900-484)
4416
47x93
(70-23)(70+23)
(702-232)
(4900-529)
4371
46x94
(70-24)(70+24)
(702-242)
(4900-576)
4324
45x95
(70-25)(70+25)
(702-252)
(4900-625)
4275
44x96
(70-26)(70+26)
(702-262)
(4900-676)
4224
43x97
(70-27)(70+27)
(702-272)
(4900-729)
4171
42x98
(70-28)(70+28)
(702-282)
(4900-784)
4116
41x99
(70-29)(70+29)
(702-292)
(4900-841)
4059
40x100
(70-30)(70+30)
(702-302)
(4900-900)
4000
39x101
(70-31)(70+31)
(702-312)
(4900-961)
3939
38x102
(70-32)(70+32)
(702-322)
(4900-1024)
3876
37x103
(70-33)(70+33)
(702-332)
(4900-1089)
3811
36x104
(70-34)(70+34)
(702-342)
(4900-1156)
3744
35x105
(70-35)(70+35)
(702-352)
(4900-1225)
3675
34x106
(70-36)(70+36)
(702-362)
(4900-1296)
3604
33x107
(70-37)(70+37)
(702-372)
(4900-1369)
3531
32x108
(70-38)(70+38)
(702-382)
(4900-1444)
3456
31x109
(70-39)(70+39)
(702-392)
(4900-1521)
3379


Base number:80
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(6400).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.
79x81
(80-1)(80+1)
(802-12)
(6400-1)
6399
78x82
(80-2)(80+2)
(802-22)
(6400-4)
6396
77x83
(80-3)(80+3)
(802-32)
(6400-9)
6391
76x84
(80-4)(80+4)
(802-42)
(6400-16)
6384
75x85
(80-5)(80+5)
(802-52)
(6400-25)
6375
74x86
(80-6)(80+6)
(802-62)
(6400-36)
6364
73x87
(80-7)(80+7)
(802-72)
(6400-49)
6351
72x88
(80-8)(80+8)
(802-82)
(6400-64)
6336
71x89
(80-9)(80+9)
(802-92)
(6400-81)
6319
70x90
(80-10)(80+10)
(802-102)
(6400-100)
6300
69x91
(80-11)(80+11)
(802-112)
(6400-121)
6279
68x92
(80-12)(80+12)
(802-122)
(6400-144)
6256
67x93
(80-13)(80+13)
(802-132)
(6400-169)
6231
66x94
(80-14)(80+14)
(802-142)
(6400-196)
6204
65x95
(80-15)(80+15)
(802-152)
(6400-225)
6175
64x96
(80-16)(80+16)
(802-162)
(6400-256)
6144
63x97
(80-17)(80+17)
(802-172)
(6400-289)
6111
62x98
(80-18)(80+18)
(802-182)
(6400-324)
6076
61x99
(80-19)(80+19)
(802-192)
(6400-361)
6039
60x100
(80-20)(80+20)
(802-202)
(6400-400)
6000
59x101
(80-21)(80+21)
(802-212)
(6400-441)
5959
58x102
(80-22)(80+22)
(802-222)
(6400-484)
5916
57x103
(80-23)(80+23)
(802-232)
(6400-529)
5871
56x104
(80-24)(80+24)
(802-242)
(6400-576)
5824
55x105
(80-25)(80+25)
(802-252)
(6400-625)
5775
54x106
(80-26)(80+26)
(802-262)
(6400-676)
5724
53x107
(80-27)(80+27)
(802-272)
(6400-729)
5671
52x108
(80-28)(80+28)
(802-282)
(6400-784)
5616
51x109
(80-29)(80+29)
(802-292)
(6400-841)
5559
50x110
(80-30)(80+30)
(802-302)
(6400-900)
5500
49x111
(80-31)(80+31)
(802-312)
(6400-961)
5439
48x112
(80-32)(80+32)
(802-322)
(6400-1024)
5376
47x113
(80-33)(80+33)
(802-332)
(6400-1089)
5311
46x114
(80-34)(80+34)
(802-342)
(6400-1156)
5244
45x115
(80-35)(80+35)
(802-352)
(6400-1225)
5175
44x116
(80-36)(80+36)
(802-362)
(6400-1296)
5104
43x117
(80-37)(80+37)
(802-372)
(6400-1369)
5031
42x118
(80-38)(80+38)
(802-382)
(6400-1444)
4956
41x119
(80-39)(80+39)
(802-392)
(6400-1521)
4879

Base number:90
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(8100).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.
89x91
(90-1)(90+1)
(902-12)
(8100-1)
8099
88x92
(90-2)(90+2)
(902-22)
(8100-4)
8096
87x93
(90-3)(90+3)
(902-32)
(8100-9)
8091
86x94
(90-4)(90+4)
(902-42)
(8100-16)
8084
85x95
(90-5)(90+5)
(902-52)
(8100-25)
8075
84x96
(90-6)(90+6)
(902-62)
(8100-36)
8064
83x97
(90-7)(90+7)
(902-72)
(8100-49)
8051
82x98
(90-8)(90+8)
(902-82)
(8100-64)
8036
81x99
(90-9)(90+9)
(902-92)
(8100-81)
8019
80x100
(90-10)(90+10)
(902-102)
(8100-100)
8000
79x101
(90-11)(90+11)
(902-112)
(8100-121)
7979
78x102
(90-12)(90+12)
(902-122)
(8100-144)
7956
77x103
(90-13)(90+13)
(902-132)
(8100-169)
7931
76x104
(90-14)(90+14)
(902-142)
(8100-196)
7904
75x105
(90-15)(90+15)
(902-152)
(8100-225)
7875
74x106
(90-16)(90+16)
(902-162)
(8100-256)
7844
73x107
(90-17)(90+17)
(902-172)
(8100-289)
7811
72x108
(90-18)(90+18)
(902-182)
(8100-324)
7776
71x109
(90-19)(90+19)
(902-192)
(8100-361)
7739
70x110
(90-20)(90+20)
(902-202)
(8100-400)
7700
69x111
(90-21)(90+21)
(902-212)
(8100-441)
7659
68x112
(90-22)(90+22)
(902-222)
(8100-484)
7616
67x113
(90-23)(90+23)
(902-232)
(8100-529)
7571
66x114
(90-24)(90+24)
(902-242)
(8100-576)
7524
65x115
(90-25)(90+25)
(902-252)
(8100-625)
7475
64x116
(90-26)(90+26)
(902-262)
(8100-676)
7424
63x117
(90-27)(90+27)
(902-272)
(8100-729)
7371
62x118
(90-28)(90+28)
(902-282)
(8100-784)
7316
61x119
(90-29)(90+29)
(902-292)
(8100-841)
7259
60x120
(90-30)(90+30)
(902-302)
(8100-900)
7200
59x121
(90-31)(90+31)
(902-312)
(8100-961)
7139
58x122
(90-32)(90+32)
(902-322)
(8100-1024)
7076
57x123
(90-33)(90+33)
(902-332)
(8100-1089)
7011
56x124
(90-34)(90+34)
(902-342)
(8100-1156)
6944
55x125
(90-35)(90+35)
(902-352)
(8100-1225)
6875
54x126
(90-36)(90+36)
(902-362)
(8100-1296)
6804
53x127
(90-37)(90+37)
(902-372)
(8100-1369)
6731
52x128
(90-38)(90+38)
(902-382)
(8100-1444)
6656
51x129
(90-39)(90+39)
(902-392)
(8100-1521)
6579

Base number:100
By using formula (a+b)(a-b)=a2-bbelow table represent easy multiplication.Here only difficult thing is subtracting square numbers from square of  base number(10000).In fourth column we are subtracting squared numbers from a square of base number. You need to practice fourth column perfectly so that you can this formula effectively.
99x101
(100-1)(100+1)
(1002-12)
(10000-1)
9999
98x102
(100-2)(100+2)
(1002-22)
(10000-4)
9996
97x103
(100-3)(100+3)
(1002-32)
(10000-9)
9991
96x104
(100-4)(100+4)
(1002-42)
(10000-16)
9984
95x105
(100-5)(100+5)
(1002-52)
(10000-25)
9975
94x106
(100-6)(100+6)
(1002-62)
(10000-36)
9964
93x107
(100-7)(100+7)
(1002-72)
(10000-49)
9951
92x108
(100-8)(100+8)
(1002-82)
(10000-64)
9936
91x109
(100-9)(100+9)
(1002-92)
(10000-81)
9919
90x110
(100-10)(100+10)
(1002-102)
(10000-100)
9900
89x111
(100-11)(100+11)
(1002-112)
(10000-121)
9879
88x112
(100-12)(100+12)
(1002-122)
(10000-144)
9856
87x113
(100-13)(100+13)
(1002-132)
(10000-169)
9831
86x114
(100-14)(100+14)
(1002-142)
(10000-196)
9804
85x115
(100-15)(100+15)
(1002-152)
(10000-225)
9775
84x116
(100-16)(100+16)
(1002-162)
(10000-256)
9744
83x117
(100-17)(100+17)
(1002-172)
(10000-289)
9711
82x118
(100-18)(100+18)
(1002-182)
(10000-324)
9676
81x119
(100-19)(100+19)
(1002-192)
(10000-361)
9639
80x120
(100-20)(100+20)
(1002-202)
(10000-400)
9600
79x121
(100-21)(100+21)
(1002-212)
(10000-441)
9559
78x122
(100-22)(100+22)
(1002-222)
(10000-484)
9516
77x123
(100-23)(100+23)
(1002-232)
(10000-529)
9471
76x124
(100-24)(100+24)
(1002-242)
(10000-576)
9424
75x125
(100-25)(100+25)
(1002-252)
(10000-625)
9375
74x126
(100-26)(100+26)
(1002-262)
(10000-676)
9324
73x127
(100-27)(100+27)
(1002-272)
(10000-729)
9271
72x128
(100-28)(100+28)
(1002-282)
(10000-784)
9216
71x129
(100-29)(100+29)
(1002-292)
(10000-841)
9159
70x130
(100-30)(100+30)
(1002-302)
(10000-900)
9100
69x131
(100-31)(100+31)
(1002-312)
(10000-961)
9039
68x132
(100-32)(100+32)
(1002-322)
(10000-1024)
8976
67x133
(100-33)(100+33)
(1002-332)
(10000-1089)
8911
66x134
(100-34)(100+34)
(1002-342)
(10000-1156)
8844
65x135
(100-35)(100+35)
(1002-352)
(10000-1225)
8775
64x136
(100-36)(100+36)
(1002-362)
(10000-1296)
8704
63x137
(100-37)(100+37)
(1002-372)
(10000-1369)
8631
62x138
(100-38)(100+38)
(1002-382)
(10000-1444)
8556
61x139
(100-39)(100+39)
(1002-392)
(10000-1521)
8479







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average of first 100 odd numbers

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LOGIC BEHIND MAGIC SQUARE

Assume a magic square of 3x3 A B C D E F G H I The above figure shows a 3x3 magic square. In the magic square sum of colum, row, diagnol numbers should be same A+B+C=D+E+F=G+H+I=A+D+G=B+E+H=C+F+I=A+E+I=C+E+G=sum A+B+C D+E+F G+H+I A+D+G B+E+H C+F+I A+E+I C+E+G By  seeing the  above there is 8 type of sum is available. Row wise-3,  column wise-3, diagnol wise-2. Condition#1: There are 8 different combinations are there with same sum in a magic square. In the above 8 combinations A=2 times, B= 3 times, C= 2 times, D=3 times E=4 times, F=3 times, G=2 times, H=3 times, I= 2 times Hence the above forms the condition#2. In simply condition#2, middle number E appears 4 times in 8 combinations. Hence row, column, diagnol sum should be equal. In 3x3 magic square we are taking numbers from 1 to 9. From 9 numbers we need to take 3 numbers. From combination f

average of first n natural numbers

The natural numbers are 1,2,3,4,5,. . . . . . now we will see the sum of natural numbers                       sum of first 3 natural numbers= 1+2+3=6 the above can be written as                      sum of first 3 natural numbers= 1+2+3=6=3(3+1)/2                      sum of first 4 natural numbers= 1+2+3+4=4(4+1)/2                      then sum of n natural numbers=1+2+3+......n terms=n(n+1)/2 then the average formula = sum of elements/no of elements                     the average of n natural numbers= sum of elements/ no of elements                                                                         =(n(n+1)/2)/n                                                                         =n(n+1)/2xn                                                                         =(n+1)/2   THE AVERAGE OF FIRST N NATURAL  NUMBERS=(n+1)/2 The average of first 5 natural numbers                                  sum of 5 natural numbers=1+2+3+4+5=15