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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 $k$?

 Aug 16, 2020
 #1
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k = 16.

 Aug 16, 2020
 #2
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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

 Aug 16, 2020

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