The value of the expression (2^(1004)+5^(1005))^2-(2^(1004)-5^(1005))^2 is $k\cdot10^{1004}$ for some positive integer $k$. What is $k$?
k = 16.
The LHS reduces to 2 x 10^1005
2 x 10^1005 =k * 10^1004
k =[2 x10^1005] / [10^1004] =2 x 10
k =20
+212 
