1.

Use an expansion formula to find the values of: i. (997)2ii. (102)2iii. (97)2iv. (1005)2

Answer»

i. (997)2 = (1000 – 3)2

Here, a = 1000 and b = 3 

(1000 – 3)2 = (1000)2 – 2 x 1000 x 3 + 32 …. [(a – b)2 = a2 – 2ab + b2 ] 

= 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 + 22 …. [(a + b)2 = a2 + 2ab + b2 ] 

= 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 + 32 …. [(a – b)2 = a2 – 2ab + b2 ] 

= 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 + 52 …. [(a + b)2 = a2 + 2ab + b2 ]

= 1000000+ 10000 + 25 

= 1010025 

∴ (1005)2 = 1010025


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