Question

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)(3x−5)
left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis

(3x+5)2
left parenthesis 3 x plus 5 right parenthesis squared

9x(x−25)

Answer 1

To find which expression is equivalent to \( 9x^2 - 25 \) using the Distributive Property, we can start by recognizing that \( 9x^2 - 25 \) is a difference of squares.

The general form for the difference of squares is:

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

In this case:

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

So, applying the difference of squares formula:

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

Now, we can check which option matches:

1. \( (4.5x + 12.5)(4.5x - 12.5) \) - Not equivalent
2. \( (3x + 5)(3x - 5) \) - **This is equivalent**
3. \( (3x + 5)^2 \) - Not equivalent
4. \( 9x(x - 25) \) - Not equivalent

The expression that is equivalent to \( 9x^2 - 25 \) is:

\[
\boxed{(3x + 5)(3x - 5)}
\]