Example−1: Find (101)2
Solution:
To find (101)2, we use identity (a + b)2 = a2 + 2ab + b2| (101)2 | = | (100 + 1)2 [Here: a = 100, b = 1] |
| = | (100)2 + 2(100)(1) + (1)2 | |
| = | 10000 + 200 + 1 | |
| = | 10201 |
Example−2: What is the value of (99)2?
Solution:
To find (99)2, we use identity (a – b)2 = a2 – 2ab + b2| (99)2 | = | (100 – 1)2 [Here: a = 100, b = 1] |
| = | (100)2 – 2(100)(1) + (1)2 | |
| = | 10000 – 200 + 1 | |
| = | 9801 |
Example−3: Find (100)2 – (99)2.
Solution:
To find (100)2 – (99)2, we use identity (a + b)(a – b) = a2 – b2.| (100)2 – (99)2 | = | (100 + 99)(100 – 99) [Here: a = 100, b = 99] |
| = | (199)(1) | |
| = | 199 |