31.
3897 x 999 = 3897 x (1000 -1)
= 3897 x 1000 – 3897 x 1
= 3897000 – 3897 = 3893103
3897000
-2519
3893103
32.
7259 x 9999 = 72519 x (10000 – 1)
= 72519 x 10000 – 72519
x 1
= 725190000 – 72519 =
72117481 725190000
-72519 
725117481
33.
2056 x 987 = 2056 x (1000 – 13)
=2056 x 1000 – 2056 x
13 2056000
=2056000 – 2672 =
2029272 - 26728
2029272
34.
1904 x 1904 = (1904)² =(1900 + 4)²
= (1900)² +
4²
+ x 21900 x 4 = 3610000 + 16 +15200
= 3610016 + 15200 =
3625216.
35.
1397 x 1397 = (1397)² = (1400 – 3)²
= (1400)² +
3²
- 2 x 1400 x 3 = 1960000 + 9 8400
190009
=1960009 – 8400 =
1951609. -8400
1951609
36.
107 x 107 +93 x 93 = (107)² +
(93)²
=(100 – 7)²
+ (100 – 7)²
= 2 x [(200)² +
(17)²
37.
(217)² + (183)² = (200 + 17)² +
(200 – 17)²
= 2[(200)² +
(17)²]
= 2 [40000 + 289] = (2x
40289) = 80578. 
38.
106 x 106 – 94 x 94 =(106)²
-(94)²
= (106 + 94) (106 – 94)
=(200 x 12) = 2400.
39.
8796 x 223 + 8796 x 77 =8796 x (223 x + 77) [by
distributive law]
(8796 x 300) =
2638800
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