To use the Distributive Property to find an equivalent expression for \(9x^2 - 25\), we recognize that the expression can be factored as a difference of squares.
The difference of squares formula is:
\[ a^2 - b^2 = (a - b)(a + b) \]
In the expression \(9x^2 - 25\), we can identify \(a^2 = 9x^2\) and \(b^2 = 25\).
Thus, we have:
- \(a = 3x\) (since \((3x)^2 = 9x^2\))
- \(b = 5\) (since \(5^2 = 25\))
Applying the difference of squares formula, we get:
\[ 9x^2 - 25 = (3x - 5)(3x + 5) \]
Now let's check the original response, which seems to imply we should consider the provided options.
If you provided \( (4.5x + 12.5)(4.5x - 12.5) \), let's see if that would simplify to match our expression.
By expanding that:
\[ (4.5x + 12.5)(4.5x - 12.5) = (4.5x)^2 - (12.5)^2 = 20.25x^2 - 156.25 \]
This does not match \(9x^2 - 25\).
So to summarize, the expression equivalent to \(9x^2 - 25\) is:
\[ (3x - 5)(3x + 5) \]
If that option is not in the responses you provided, then none of the options given is the correct equivalent expression.