(i) 512
= (50 + 1)2
Taking a = 50 and b = 1 we get
(a + b)2 = a2 + 2ab + b2
(50 + 1)2 = 502 + 2 (50) (1) + 12
= 2500 + 100 + 1
512 = 2601
(ii) 1032
1032 = (100 + 3)2
Taking a = 100 and b = 3
(a + b)2 = a2 + 2ab + b2 becomes
(100 + 3)2 = 1002 + 2 (100) (3) + 32
= 10000 + 600 + 9
1032 = 10609
(iii) 9982
9982 = (1000 – 2)2
Taking a = 1000 and b = 2
(a – b)2 = a2 + 2ab + b2 becomes
(1000 – 2)2 = 10002 – 2 (1000) (2) + 22
= 1000000 – 4000 + 4
9982 = 10,04,004
(iv) 472
472 = (50 – 3)2
Taking a = 50 and b = 3
(a – b)2 = a2 – 2ab + b2 becomes
(50 – 3)2 = 502 – 2 (50) (3) + 32
= 2500 – 300 + 9 = 2200 + 9
472 = 2209
