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

Responses

(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)
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

1 answer

To use the Distributive Property and factor the expression \(9x^2 - 25\), we recognize that this expression is a difference of squares.

The difference of squares can be factored using the formula: \[ a^2 - b^2 = (a + b)(a - b) \]

In the expression \(9x^2 - 25\):

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

Thus, we can factor \(9x^2 - 25\) as follows: \[ 9x^2 - 25 = (3x + 5)(3x - 5) \]

From the provided options, the expression that is equivalent to \(9x^2 - 25\) is: \[ (3x + 5)(3x - 5) \]

So the correct response is: (3x + 5)(3x − 5)