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

(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)

1 answer

To find the expression equivalent to \( 9x^2 - 25 \) using the Distributive Property, we can recognize that this expression resembles the difference of squares, which can be factored as \( a^2 - b^2 = (a - b)(a + b) \).

Here, we can see:

  • \( 9x^2 \) is \( (3x)^2 \)
  • \( 25 \) is \( 5^2 \)

Thus, we can factor \( 9x^2 - 25 \) as follows:

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

Using the difference of squares formula:

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

Now, we can compare our result with the given options. The correct expression equivalent to \( 9x^2 - 25 \) is:

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

So, the correct response is:

(3x+5)(3x−5)