(i) (102)2
This can be written as:
(100 + 2)2
= (100)2 + 2 (100) (2) + 22
= 10000 + 400 + 4
= 10404
(ii) (99)2
This can be written as:
(100 – 1)2
= (100)2 – 2 (100) (1) + 12
= 10000 – 200 + 1
= 9801
(iii) (1001)2
This can be written as:
(1000 + 1)2
= (1000)2 + 2 (1000) (1) + 12
= 1000000 + 2000 + 1
= 1002001
(iv) (999)2
This can be written as:
(1000 – 1)2
= (1000)2 – 2 (1000) (1) + 12
= 1000000 – 2000 + 1
= 998001
(v) (703)2
This can be written as:
(700 + 3)2
= (700)2 + 2 (700) (3) + 32
= 490000 + 4200 + 9
= 494209