Fewpal
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Use the formula to find the values: 

i. 502 × 498 

ii. 97 × 103

iii. 54 × 46 

iv. 98 × 102

1 Answer

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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

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