# 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) 395

(ii) 995

(iii) 495

(iv) 498

(v) 99

(vi) 999

(vii) 599

Solution:

(i) Decomposing: 395 = 400 − 5

Here, a = 400 and b = 5

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

3952 = (400  5)2 = 400 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 = 1000 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 = 600 2(600)(1) + 12 = 360000  1200 + 1 = 358801