Question

Use an expansion formula to find the values of: 

i. (997)²

ii. (102)²

iii. (97)²

iv. (1005)²

Answer 1

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