Use the Distributive Property to find which expression is equivalent to 9x^2−25 .(1 point)

Responses

(3x+5)^2

(3x+5)(3x−5)

(4.5x+12.5)(4.5x−12.5)

9x(x−25)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To find the expression equivalent to \( 9x^2 - 25 \) using the Distributive Property (also known as factoring), we can recognize that \( 9x^2 - 25 \) is a difference of squares. The difference of squares formula states that:

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

In this case, we can identify \( a = 3x \) and \( b = 5 \), since:

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

So we can apply the difference of squares formula:

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

Now looking at the options provided, the expression that is equivalent to \( 9x^2 - 25 \) is:

**(3x+5)(3x−5)**

So, the correct response is **(3x+5)(3x−5)**.