Using identities, find the value of
(i) 1012
(ii) 982
(iii) (0.98)2
(iv) 11 × 9
(v) 190 × 190 - 10 × 10
(i) 1012 = (100 + 1)2
= 1002 + 2 × 100 × 1 + 12
= 10000 + 200 + 1 = 10201
(ii) 982 = (100 - 2)2
= 1002 - 2 × 100 × 2 + 22
= 10000 - 400 + 4 = 9604
(iii) 0.982 = (1 - 0.02)2
= 12 - 2 × 1 × 0.02 + (0.02)2
= 1 - 0.04 + 0.0004
= 0.9604
(iv) 11 × 9 = (10+1) (10-1)
= 102 - 12
= 99
(v) 190 × 190 - 10 × 10 = 1902 - 102
= (190 + 10) (190 - 10)
= 200 × 180
= 36000