Question

The value of (105)${}^2$ + (95)${}^2$ is:

• A. 39900
• B. 41889
• C. 34649
• D. 40229

Answer 1

The correct option is A 39900

(105)${}^2$ can be written as (100+5)${}^2$,
(95)${}^2$ can be written as (100-5)${}^2$.
Using the identity (a+b)${}^2$ + (a-b)${}^2$ = 4ab,
(105)${}^2$ + (95)${}^2$ = 4(105)(95) = 39900.