Bot GPT 4-o mini To find the expression equivalent to \( 9x^2 - 25 \) using the Distributive Property, we recognize that this expression is a difference of squares, which follows the formula:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can rewrite \( 9x^2 - 25 \) as follows:
\[ 9x^2 - 25 = (3x)^2 - 5^2 \]
Here, \( a = 3x \) and \( b = 5 \). According to the difference of squares formula, we can factor this expression as:
\[ (3x - 5)(3x + 5) \]
Now, let's evaluate the options:
A. \( (3x + 5)^2 \) - This is not correct. B. \( (4.5x + 12.5)(4.5x - 12.5) \) - This does not match our factorization. C. \( (3x + 5)(3x - 5) \) - This matches our factorization. D. \( 9x(x - 25) \) - This does not match our factorization.
Therefore, the correct answer is:
C. \( (3x + 5)(3x - 5) \).
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