To use the distributive property to factor the expression \(9x^2 - 25\), we can recognize that it is a difference of squares. The general form for factoring a difference of squares \(a^2 - b^2\) is \((a + b)(a - b)\).
In this case:
- \(9x^2\) can be expressed as \((3x)^2\).
- \(25\) can be expressed as \(5^2\).
Therefore, we can rewrite \(9x^2 - 25\) as: \[ (3x)^2 - 5^2 \]
Applying the difference of squares formula, we get: \[ (3x + 5)(3x - 5) \]
Now, let's compare this result with the answer choices provided:
A. \((3x+5)(3x-5)\) - This matches our factored expression.
B. \((4.5x+12.5)(4.5x-12.5)\) - This does not match.
C. \(9x(x-25)\) - This does not match.
D. \((3x+5)^2\) - This does not match.
The expression that is equivalent to \(9x^2 - 25\) is: A. \((3x+5)(3x-5)\).