To use the Distributive Property to find an equivalent expression for \( 9x^2 - 25 \), we can recognize that this expression is a difference of squares. It can be factored using the identity \( a^2 - b^2 = (a - b)(a + b) \).
In this case, we can rewrite \( 9x^2 - 25 \) as:
\[ (3x)^2 - (5)^2 \]
Applying the difference of squares formula, we have:
\[ 9x^2 - 25 = (3x - 5)(3x + 5) \]
Now, let's look at the options provided:
A) \( 9x(x - 25) \) - This is incorrect.
B) \( (3x + 5)^2 \) - This is incorrect as it expands to \( 9x^2 + 30x + 25 \).
C) \( (4.5x + 12.5)(4.5x - 12.5) \) - This is incorrect, as it expands to \( 20.25x^2 - 156.25 \).
D) \( (3x + 5)(3x - 5) \) - This is correct, as shown above.
Therefore, the correct answer is: D) (3x + 5)(3x - 5).