Final answer:
The expression 36x² - 25 is equivalent to option B) (18x)² - (5)².
Step-by-step explanation
To determine the equivalent expression, observe the given expression: 36x² - 25. This expression can be rewritten as the difference of squares, following the formula: a² - b² = (a + b)(a - b). Applying this formula to the expression, 36x² - 25, it can be expressed as (6x)² - 5². Simplifying this further, it becomes (6x + 5)(6x - 5).
Now compare this result with the given options. Option A, (18x)² + (-5)², doesn't fit as it represents the sum of squares, not a difference of squares. Option C suggests both sum and difference of squares, which isn't accurate for the given expression. Option D claims none of the expressions match, which isn't correct as option B indeed represents the correct difference of squares equivalent to the given expression.
Therefore, after applying the difference of squares formula to the expression 36x² - 25, it simplifies to (6x + 5)(6x - 5), which matches the structure of option B, (18x)² - (5)², signifying that option B is the equivalent expression for 36x² - 25.