To determine which expression is equivalent to \( 9n^2 - 25 \), we can recognize that this is a difference of squares. The difference of squares formula is:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can rewrite \( 9n^2 - 25 \) as:
\[ (3n)^2 - 5^2 \]
Here, \( a = 3n \) and \( b = 5 \). Applying the difference of squares formula, we have:
\[ 9n^2 - 25 = (3n - 5)(3n + 5) \]
Now, we will look at the options provided:
- Q: \( 9(n-4)^2 \)
- H: \( (3n + 5)(3n - 5) \)
- J: \( 9(n + 4)(n - 4) \)
- F: \( (3n - 5)^2 \)
The expression that matches our factorization is:
H: \( (3n + 5)(3n - 5) \)
Therefore, the correct answer is:
H