Use the Distributive Property to find which expression is

To determine which expression is equivalent to \(9x^2 - 25\) using the Distributive Property (also known as the FOIL method for binomials), we can identify that \(9x^2 - 25\) is a difference of squares, which can be factored as follows:

\[
a^2 - b^2 = (a + b)(a - b)
\]

In this case, we have:

\[
a = 3x \quad \text{and} \quad b = 5
\]

So:

\[
9x^2 - 25 = (3x)^2 - 5^2 = (3x + 5)(3x - 5)
\]

Now let's look at the provided options:

1. \((3x + 5)(3x - 5) \) - This is equivalent to \(9x^2 - 25\).
2. \(9x(x - 25)\) - This expands to \(9x^2 - 225x\), which is not equivalent to \(9x^2 - 25\).
3. \((3x + 5)^2\) - This expands to \(9x^2 + 30x + 25\), which is not equivalent to \(9x^2 - 25\).
4. \((4.5x + 12.5)(4.5x - 12.5)\) - This does not relate to \(9x^2 - 25\) and expands differently.

Therefore, the correct expression equivalent to \(9x^2 - 25\) is:

\((3x + 5)(3x - 5)\)