To find an equivalent expression for \(9x^2 - 25\) using the Distributive Property, we can recognize that \(9x^2 - 25\) can be factored as a difference of squares. The difference of squares formula is:
\[ a^2 - b^2 = (a - b)(a + b) \]
In our expression \(9x^2 - 25\):
- \(a^2 = 9x^2\) which means \(a = 3x\)
- \(b^2 = 25\) which means \(b = 5\)
Using the difference of squares formula, we can factor \(9x^2 - 25\) as follows:
\[ 9x^2 - 25 = (3x - 5)(3x + 5) \]
Now let's check the options provided:
- A. \(9x(x - 25)\) (not correct)
- B. \((4.5x + 12.5)(4.5x - 12.5)\) (not correct)
- C. \((3x + 5)(3x - 5)\) (this matches what we found)
- D. \((3x + 5)^2\) (not correct)
The correct equivalent expression is:
C. (3x + 5)(3x - 5)