Question

Using suitable identity, evaluate the following

(i) 103³

(ii) 101 x 102

(iii) 999²

Answer 1

(i) 103³

= (100 + 3)³

= (100)³ + (3)³ + 3 x 100 x 3 x (100 + 3)

= 1000000 + 27 + 900 (103)

= 1000027 + 92700

= 1092727

(ii) 101 x 102

= (100 + 1) (100 + 2)

= (100) + 100(1 + 2) + 1 x 2

= 10000 + 300 + 2

= 10302

(iii) (999)²

= (1000 - 1)²

= (1000)² + (1)² - 2 x 1000 x 1

= 1000000 + 1 - 2000

= 998001