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

1 answer

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

The general form for a difference of squares is:

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

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

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

Applying the difference of squares formula gives us:

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

Now, we can match this expression with the options provided. The correct equivalent expression to \( 9x^2 - 25 \) is:

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

So the correct response is:

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