Use the formula to find the values: i. 502 × 498 ii. 97 × 103iii.

1.	Use the formula to find the values: i. 502 × 498 ii. 97 × 103iii. 54 × 46 iv. 98 × 102
Answer» 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

Use the formula to find the values: i. 502 × 498 ii. 97 × 103iii. 54 × 46 iv. 98 × 102

Answer»

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