Use the Distributive Property to find which expression is equivalent to 9x2−25 .(1 point)

Responses

9x(x−25)
9 x left parenthesis x minus 25 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

(4.5x+12.5)(4.5x−12.5)

1 answer

To solve for an expression equivalent to \( 9x^2 - 25 \) using the Distributive Property, we can recognize that this expression resembles the difference of squares. Specifically, it can be factored using the identity \( a^2 - b^2 = (a - b)(a + b) \).

In this case, we can identify \( 9x^2 \) as \( (3x)^2 \) and 25 as \( 5^2 \). Thus, we rewrite it as:

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

Applying the difference of squares formula:

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

So, the expression that is equivalent to \( 9x^2 - 25 \) is:

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

Which corresponds to the second option in your responses:

(3x + 5)(3x - 5).