Giant Binomial Squared

The sum of the digits in base ten of (10(4n2 +8) +1)2, where n is a positive integer, is:

  1. 4
  2. 4n
  3. 2 + 2n
  4. 4n2
  5. n2 + n + 2


Show/Hide Solution

(10(4n2 +8) +1) will look like this 1000…00001; that is, a number with a 1 on each end and 0’s in between.

If we square it, we have

  10…01  
x 10…01  
  10…01  
+ 10…010  …  0  
10…1..1…01  or possibly
10…2…01  

So the sum of the digits is 4, answer (a).

The 4n2 + 8 is a total red herring.

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