To use the Distributive Property (also known as the FOIL method for binomials) to find an expression equivalent to \(9x^2 - 25\), we need to recognize that \(9x^2 - 25\) is a difference of squares, which can be factored as:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can write \(9x^2 - 25\) as:
\[ (3x)^2 - 5^2 \]
Using the difference of squares formula:
\[ (3x - 5)(3x + 5) \]
Now, let's analyze the provided options:
- \((4.5x + 12.5)(4.5x - 12.5)\) does not match.
- \((3x + 5)(3x - 5)\) matches our factorization.
- \(9x(x - 25)\) does not match because it's not a correct factorization.
- \((3x + 5)^2\) is also not a match.
Thus, the expression equivalent to \(9x^2 - 25\) is:
\((3x + 5)(3x - 5)\).