To find which expression is equivalent to \( 9x^2 - 25 \) using the Distributive Property, we can recognize that this expression is a difference of squares. The difference of squares formula is:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can identify:
- \( a = 3x \) (since \( (3x)^2 = 9x^2 \))
- \( b = 5 \) (since \( 5^2 = 25 \))
Thus, we can rewrite \( 9x^2 - 25 \) as:
\[ (3x)^2 - 5^2 = (3x - 5)(3x + 5) \]
Now, let's evaluate the options:
A. \( (3x+5)(3x-5) \) - This matches our factorization, so it’s equivalent to \( 9x^2 - 25 \).
B. \( (4.5x + 12.5)(4.5x - 12.5) \) - Does not match our factorization.
C. \( 9x(x - 25) \) - This does not correctly match the expression.
D. \( (3x + 5)^2 \) - This expands to \( 9x^2 + 30x + 25 \), which is not equivalent.
Thus, the correct answer is:
A. \( (3x+5)(3x-5) \).