If the quantity 6^2+ 6^4 + 6^6 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 correct answer:  A) 52  B) 15  C) 36  D) 22  E) 25
(a+b)(a-b) = a^2 - b^2   6^2+ 6^4 + 6^6 = 6^2 (1+6^2+6^4)   if the above expression is solved even then every term of the expression will remain a multiple of 6^2 which is out of parenthesis   hence, b must be a multiple of 6^2 i.e. 36   Answer: option 36
<result>C</result>
If the quantity 6^2+ 6^4 + 6^6 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?