Question

Find the squares of the following numbers using the identity (a − b)² = a² − 2ab + b²:
(i) 395
(ii) 995
(iii) 495
(iv) 498
(v) 99
(vi) 999
(vii) 599

Answer 1

(i) Decomposing: 395 = 400 − 5
Here, a = 400 and b = 5
Using the identity (a − b)² = a² − 2ab + b²:
395² = (400 − 5)² = 400² − 2(400)(5) + 5² = 160000 − 4000 + 25 = 156025

(ii) Decomposing: 995 = 1000 − 5
Here, a = 1000 and b = 5
Using the identity (a − b)² = a² − 2ab + b²:
995² = (1000 − 5)² = 1000² − 2(1000)(5) + 5² = 1000000 − 10000 + 25 = 990025

(iii) Decomposing: 495 = 500 − 5
Here, a = 500 and b = 5
Using the identity (a − b)² = a² − 2ab + b²:
495² = (500 − 5)² = 500² − 2(500)(5) + 5² = 250000 − 5000 + 25 = 245025

(iv) Decomposing: 498 = 500 − 2
Here, a = 500 and b = 2
Using the identity (a − b)² = a² − 2ab + b²:
498² = (500 − 2)² = 500² − 2(500)(2) + 2² = 250000 − 2000 + 4 = 248004

(v) Decomposing: 99 = 100 − 1
Here, a = 100 and b = 1
Using the identity (a − b)² = a² − 2ab + b²:
99² = (100 − 1)² = 100² − 2(100)(1) + 1² = 10000 − 200 + 1 = 9801

(vi) Decomposing: 999 = 1000 - 1
Here, a = 1000 and b = 1
Using the identity (a − b)² = a² − 2ab + b²:
999² = (1000 − 1)² = 1000² − 2(1000)(1) + 1² = 1000000 − 2000 + 1 = 998001

(vii) Decomposing: 599 = 600 − 1
Here, a = 600 and b = 1
Using the identity (a − b)² = a² − 2ab + b²:
599² = (600 − 1)² = 600² − 2(600)(1) + 1² = 360000 − 1200 + 1 = 358801