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1. Question 1.
Find the following products :
Solution:

3. Question 2.
Evaluate the following :
(i) 102 x 106
(ii) 109 x 107
(iii) 35 x 37
(iv) 53 x 55
(v) 103 x 96
(vi) 34 x 36
(vii) 994 x 1006
Solution:
(i) 102 x 106 = (100 + 2) (100 + 6)
= (100)2
+ (2 + 6) x 100 + 2 x 6
= 10000 + 800 + 12 = 10812
(ii) 109 x 107 = (100 + 9) (100 + 7)
= (100)2
+ (9 + 7) x 100 + 9 x 7
=10000 + 1600 + 63 = 11663

4. (iii) 35 x 37 = (30 + 5) (30 + 7)
= (30)2
+ (5 + 7) x 30 + 5 x 7
= 900 + 12 x 30 + 35
= 900 + 360 + 35 = 1295
(iv) 53 x 55 = (50 + 3) (50 + 5)
= (50)2
+ (3 + 5) x 50 + 3 x 5
= 2500 + 8 x 50 + 15
= 2500 + 400+ 15 = 2915
(v)103 x 96 = (100 + 3) (100-4)
= (100)2
+ (3 – 4) x 100 + 3 x (-4)
= 10000+ (-1) x 100-12
= 10000 – 100 – 12 = 10000 – 112 = 9888
(vi) 34 x 36 = (30 + 4) (30 + 6)
= (30)2
+ (4 + 6) x 30 + 4 x 6
= 900 + 10 x 30 + 24
= 900 + 300 + 24 = 1224
(vii) 994 x 1006 = (1000 – 6) (1000 + 6)
= (1000)2
+ (-6 + 6) x 1000 + (-6) x 6
= 1000000 + 0-36
= 1000000-36 = 999964