Final answer:
To factor completely the expression 25x²−36, we can use the difference of squares formula (a² - b² = (a + b)(a - b)). In this case, the correct factorization is (5x - 6)(5x + 6).
Step-by-step explanation:
To factor completely the expression 25x²−36, we can use the difference of squares formula. The formula states that a² - b² can be factored as (a + b)(a - b). In this case, we have 25x² - 36, which can be rewritten as (5x)² - 6².
Using the difference of squares formula, we have (5x + 6)(5x - 6). Therefore, the correct factorization is option D) (5x - 6)(5x + 6).