Question

Using identities, evaluate the following

(i) 99²
(ii) 103²
(iii) 297 x 303
(iv) 78 x 82

Answer 1

(i) 99²

= (100 – 1)²

= (100)² – 2 (100) (1) + (1)² (Using identity II)

= 10000 – 200 + 1

= 10000 + 1 – 200

= 10001 – 200

= 9801

(ii) 103²

= (100 + 3)²

= (100)² + 2 (100) (3) + (3)² (Using identity I)

= 10000 + 600 + 9

= 10609

(iii) 297 x 303

= (300 – 3) x (300 + 3)

= (300)² – (3)² (Using identity III)

= 90000 – 9

= 89991

(iv) 78 x 82

= (80 – 2) x (80 + 2)

= (80)² – (2)² (Using identity III)

= 6400 – 4

= 6396