Question

Use the formula to find the values: 

i. 502 × 498 

ii. 97 × 103 

iii. 54 × 46 

iv. 98 × 102

Answer 1

i. 502 × 498 = (500 + 2) (500 – 2) 

Here, a = 500, b = 2 

∴ (500 + 2) (500 – 2) = 500² – 2² 

…. [(a + b)(a – b) = a² – b²] 

= 250000 – 4

= 249996 

∴ 502 × 498 = 249996

ii. 97 × 103 = (100 – 3) (100 + 3) 

Here, a = 100, b = 3 

∴ (100 – 3) (100 + 3) = 100² – 3² 

…. [(a + b)(a – b) = a² – b²] 

= 10000 – 9 

= 9991 

∴ 97 × 103 = 9991

iii. 54 × 46 = (50 + 4) (50 – 4) 

Here, a = 50, b = 4 

∴ (50 + 4) (50 – 4) = 50² – 4² 

…. [(a + b)(a – b) = a² – b²] 

= 2500 – 16 = 2484 

∴ 54 × 46 = 2484

iv. 98 × 102 = (100 – 2) (100 + 2) 

Here, a = 100, b = 2 

∴ (100 – 2) (100 + 2) 

= 100² – 2²

…. [(a + b)(a – b) = a² – b²] 

= 10000 – 4 

= 9996 

∴ 98 × 102 = 9996