Question

use the expansion formula and find the value of [97]square​

Answer 1

Answer:

(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 = 1010025Read more on Sarthaks.com - https://www.sarthaks.com/862554/use-an-expansion-formula-to-find-the-values-of-i-997-2-ii-102-2-iii-97-2-iv-1005-2