Evaluate : 20142015×20152014 – 20142014 ×20152015

Answer 1

without a calculator...

let a=20142014
then 20142015 = a+1
then 20152015 = a + 1 + 1000 = a+1001
then 20152014 = a+1000
20142015×20152014 – 20142014 ×20152015

= (a+1)(a+1000) - a(a+1001)
= a^2 + 1001a + 1000 - a^2 - 1001a
= 1000

Answer 2

letx=20142014
then 20142015=x+1
then 20152014=x+10000
then 20152015=x+10001

20142015×20152014-20142014×20152015
=(x+1)(x+10000)-x(x+10001)
= x²+10001x+10000-x²-10001x
= 10000

Answer 3

10000