To use the Distributive Property on the expression \(9x^2 - 25\), we note that it has the form of a difference of squares. This can be expressed as:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can identify:
\[ a = 3x \quad \text{and} \quad b = 5 \]
Thus, we have:
\[ 9x^2 - 25 = (3x)^2 - 5^2 \]
Applying the difference of squares formula, we get:
\[ 9x^2 - 25 = (3x - 5)(3x + 5) \]
We compare this result with the provided options:
- \((3x + 5)^2\) - This expands to \(9x^2 + 30x + 25\), which does not match.
- \((4.5x + 12.5)(4.5x - 12.5)\) - This is also a difference of squares, but since \(4.5^2\) and \(12.5^2\) do not yield \(9\) and \(25\), this option does not apply.
- \(9x(x - 25)\) - This expands to \(9x^2 - 225x\), which does not match.
- \((3x + 5)(3x - 5)\) - This expands to \(9x^2 - 25\), which matches our original expression.
Therefore, the correct expression that is equivalent to \(9x^2 - 25\) is:
\[ \boxed{(3x + 5)(3x - 5)} \]
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