If the quantity 3^4+ 3^6 + 3^8 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
Choose the most appropriate option.
A) 57 B) 26 C) 52 D) 81 E) 25
(a+b)(a-b) = a^2 - b^2   3^4+ 3^6 + 3^8 = 3^4 (1+3^2+3^4)   if the above expression is solved even then every term of the expression will remain a multiple of 3^4 which is out of parenthesis   hence, b must be a multiple of 3^4 i.e. 81   Answer: option 81
<result>D</result>
If the quantity 3^4+ 3^6 + 3^8 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?