(i) 297 x 303
297 x 303 = (300 – 3) (300 + 3)
Taking a = 300 and b = 3, then
(a + b) (a – b) = a2 – b2 becomes
(300 + 3) (300 – 3) = 3002 – 32
303 x 297 = 90000 – 9
297 x 303 = 89,991
(ii) 990 x 1010
990 x 1010 = (1000 – 10) (1000 + 10)
Taking a = 1000 and b = 10, then
(a – b) (a + b) = a2 – b2 becomes
(1000 – 10) (1000 + 10) = 10002 – 102
990 x 1010 = 1000000 – 100
990 x 1010 = 999900
(iii) 51 x 52
= (50 + 1) (50 + 1)
Taking x = 50, a = 1 and b = 2
Then (x + a) (x + b) = x2 + (a + b) x + ab becomes
(50 + 1) (50 + 2) = 502 + (1 + 2) 50 + (1 × 2)
2500 + (3) 50 + 2 = 2500 + 150 + 2
51 x 52 = 2652