Question

Observe the following pattern

2^{2 _} 1² = 2+1

3² - 2² = 3+2

4² - 3² = 4+3

5² - 4² = 5+4

And find the value of

(i) 100² -99² 

(ii) 111²-109² 

(iii)99² -96²

Answer 1

(i) 100² – 99² 

= 100 + 99 

= 199 

(ii) 111² - 109² 

= 111² – 110² + 110² - 109² 

= (111 + 110) + (110 + 109) 

= 440 

(iii) 99² - 96² = 99² – 98² + 98² – 97² + 97² - 96² 

= (99 + 98) + (98 + 92) + (97 + 96) 

= 585