Evaluate the following, using suitable identity.(i) 297 x 303 (ii) 99

1.	Evaluate the following, using suitable identity.(i) 297 x 303 (ii) 990 x 1010 (iii) 51 x 52
Answer» (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

Evaluate the following, using suitable identity.(i) 297 x 303 (ii) 990 x 1010 (iii) 51 x 52

Answer»

(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