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

1 answer

To factor the expression \( 9x^2 - 25 \) using the Distributive Property, we recognize that it is a difference of squares. The structure of a difference of squares is given by:

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

In this case, we can identify:

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

Applying the difference of squares formula:

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

Thus, the equivalent expression is:

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

So, the correct response is:

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