i. (997)^{2} = (1000 – 3)^{2}

Here, a = 1000 and b = 3

(1000 – 3)^{2 }= (1000)^{2} – 2 x 1000 x 3 + 3^{2} …. [(a – b)^{2} = a^{2} – 2ab + b^{2} ]

= 1000000 – 6000 + 9

= 994009

∴ (997)^{2} = 994009

ii. (102)^{2} = (100 + 2)^{2}

Here, a = 100 and b = 2

(100 + 2)^{2} = (100)^{2} + 2 x 100 x 2 + 2^{2} …. [(a + b)^{2} = a^{2} + 2ab + b^{2} ]

= 10000 + 400 + 4

= 10404

∴ (102)^{2} = 10404

iii. (97)^{2} = (100 – 3)^{2}

Here, a = 100 and b = 3

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

= 10000 – 600 + 9

= 9409

∴ (97)^{2} = 9409

iv. (1005)^{2} = (1000 + 5)^{2}

Here, a = 1000 and b = 5

(1000 + 5)^{2} = (1000)^{2} + 2 x 1000 x 5 + 5^{2} …. [(a + b)^{2} = a^{2} + 2ab + b^{2} ]

= 1000000+ 10000 + 25

= 1010025

∴ (1005)^{2} = 1010025