Factor 25x ^2 + 10x + 1.
(25x + 1)(x + 1)
(5x + 1)(5x - 1)
(5x + 1)²

The correct answer is:  [C]:  " (5x + 1)² " .

Explanation:

Choice [A] is incorrect: "(25x+1)(x+1) = 25x² +25x +1x +1 = 25x² + 26x + 1 .

Choice [B] is incorrect: "(5x+1)(5x-1)= 25x² -5x+5x -1 = 25x² - 1 .

This leaves us with:  Answer choice:  [C]:  " (5x + 1)² "  ;
                                                       →   as the correct answer.

However, let us work through this answer choice:

  (5x + 1)² = (5x + 1)(5x + 1) = 25x² + 5x + 5x + 1 ;
                                             = 25x²  + 10x + 1 ; which is the
                                                    expression provided in question;

So the correct answer is:  [C]:  " (5x + 1)² " .