How can you solve this problem faster?

[oxvt]

1001^2-999^2 / 101^2-99^2

A) 10
B) 20
C) 40
D) 80
E) 100

[farooq]

1001^2-999^2 / 101^2-99^2

A) 10
B) 20
C) 40
D) 80
E) 100

I took 1 min

use formula a^2 - b^2 = (a+b)(a-b)

(1001-999)(1001+999)/(101-99)(101+99) =10.

[krisraam]

(a+b)^2 + (a-b)^2 = 4ab

(1000 + 1)^2 + (1000 -1)^2 = 4*1000 *1

Thanks
raama

[kamu]

(a+b)^2 + (a-b)^2 = 4ab

(1000 + 1)^2 + (1000 -1)^2 = 4*1000 *1

Thanks
raama

I think you meant (a+b)^2 - (a-b)^2 = 4ab

and

(a+b)^2 + (a-b)^2 = 2(a^2 +b^2)