# Find the squares of the following numbers using the identity

Question:

Find the squares of the following numbers using the identity (a + b)2 = a2 + 2ab + b2:
(i) 405

(ii) 510

(iii) 1001

(iv) 209

(v) 605

Solution:

(i) On decomposing:

405 = 400 + 5

Here, a = 400 and b = 5

Using the identity (a + b)2 = a2 + 2ab + b2:

4052 = (400 + 5)2 = 4002 + 2(400)(5) + 52 = 160000 + 4000 + 25 = 164025

(ii) On decomposing:

510 = 500 + 10

Here, a = 500 and b = 10

Using the identity (a + b)2 = a2 + 2ab + b2:

5102 = (500 + 10)2 = 5002 + 2(500)(10) + 102 = 250000 + 10000 + 100 = 260100

(iii) On decomposing:

1001 = 1000 + 1

Here, a = 1000 and b = 1

Using the identity (a + b)2 = a2 + 2ab + b2:

10012 = (1000 + 1)2 = 10002 + 2(1000)(1) + 12 = 1000000 + 2000 + 1 = 1002001

(iv) On decomposing:

209 = 200 + 9

Here, a = 200 and b = 9

Using the identity (a + b)2 = a2 + 2ab + b2:

2092 = (200 + 9)2 = 2002 + 2(200)(9) + 92 = 40000 + 3600 + 81 = 43681

(v) On decomposing:

605 = 600 + 5

Here, a = 600 and b = 5

Using the identity (a + b)2 = a2 + 2ab + b2:

6052 = (600 + 5)2 = 6002 + 2(600)(5) + 52 = 360000 + 6000 + 25 = 366025