i. 502 × 498 = (500 + 2) (500 – 2)

Here, a = 500, b = 2

∴ (500 + 2) (500 – 2) = 500^{2 } – 2^{2 } …. [(a + b)(a – b) = a^{2 } – b^{2 }]

= 250000 – 4

= 249996

∴ 502 × 498 = 249996

ii. 97 × 103 = (100 – 3) (100 + 3)

Here, a = 100, b = 3

∴ (100 – 3) (100 + 3) = 100^{2 } – 3^{2 } …. [(a + b)(a – b) = a^{2 } – b^{2 }]

= 10000 – 9

= 9991

∴ 97 × 103 = 9991

iii. 54 × 46 = (50 + 4) (50 – 4)

Here, a = 50, b = 4

∴ (50 + 4) (50 – 4) = 50^{2 } – 4^{2 } …. [(a + b)(a – b) = a^{2 } – b^{2 }]

= 2500 – 16

= 2484

∴ 54 × 46 = 2484

iv. 98 × 102 = (100 – 2) (100 + 2)

Here, a = 100, b = 2

∴ (100 – 2) (100 + 2) = 100^{2 }– 2^{2 } …. [(a + b)(a – b) = a^{2 } – b^{2 }]

10000 – 4

= 9996

∴ 98 × 102 = 9996