Observe the following pattern22 _ 12 = 2+132 - 22 = 3+242 - 32 =

1.	Observe the following pattern22 _ 12 = 2+132 - 22 = 3+242 - 32 = 4+352 - 42 = 5+4And find the value of(i) 1002 -992 (ii) 1112-1092 (iii)992 -962
Answer» (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

Observe the following pattern22 _ 12 = 2+132 - 22 = 3+242 - 32 = 4+352 - 42 = 5+4And find the value of(i) 1002 -992 (ii) 1112-1092 (iii)992 -962

Answer»

(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