Question

The value of (101)${}^2$ - (99)${}^2$ is:

• A. 39996
• B. 33596
• C. 32496
• D. 36646

Answer 1

The correct option is A 39996

(101)${}^2$ can be written as (100+1)${}^2$,
(99)${}^2$ can be written as (100-1)${}^2$.
Using the identity (a+b)${}^2$ - (a-b)${}^2$ = 4ab,
$(100+1{)}^2-(100-1{)}^2=4\left(100\right)\left(1\right)=400$