Use the Distributive Property to find which expression is equivalent to 9x2−25 .(1 point) Responses (4.5x+12.5)(4.5x−12.5) left parenthesis 4.5 x plus 12.5 right parenthesis left parenthesis 4.5 x minus 12.5 right parenthesis (3x+5)2 left parenthesis 3 x plus 5 right parenthesis squared (3x+5)(3x−5) left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis 9x(x−25)

Answer 1

To find an equivalent expression for \( 9x^2 - 25 \) using the Distributive Property, we can recognize that this expression is a difference of squares. The difference of squares can be factored using the formula:

\[ a^2 - b^2 = (a + b)(a - b) \]

In this case:

• \( a^2 = 9x^2 \) which implies \( a = 3x \)
• \( b^2 = 25 \) which implies \( b = 5 \)

So, we can rewrite \( 9x^2 - 25 \) as:

\[ (3x)^2 - 5^2 \]

Using the difference of squares formula:

\[ 9x^2 - 25 = (3x + 5)(3x - 5) \]

Among the response options given, the equivalent expression is:

\[ (3x + 5)(3x - 5) \]

So the correct answer is:

(3x+5)(3x−5)