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

Question

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

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

(3x+5)(3x−5)

Answer 1

To determine which expression is equivalent to \( 9x^2 - 25 \) using the Distributive Property, let's analyze the options:

1. \( 9x(x - 25) \):

   • We can distribute \( 9x \) to both terms inside the parentheses: \[ 9x(x - 25) = 9x^2 - 225x \]
   • This does not match \( 9x^2 - 25 \).

2. \( (4.5x + 12.5)(4.5x - 12.5) \):

   • This is in the form of a difference of squares, which we can expand: \[ (a + b)(a - b) = a^2 - b^2 \] where \( a = 4.5x \) and \( b = 12.5 \): \[ (4.5x)^2 - (12.5)^2 = 20.25x^2 - 156.25 \]
   • This does not match \( 9x^2 - 25 \).

3. \( (3x + 5)^2 \):

   • Expanding \( (3x + 5)^2 \): \[ (3x + 5)(3x + 5) = 9x^2 + 30x + 25 \]
   • This does not match \( 9x^2 - 25 \).

4. \( (3x + 5)(3x - 5) \):

   • Using the difference of squares formula again: \[ (3x)^2 - (5)^2 = 9x^2 - 25 \]
   • This matches \( 9x^2 - 25 \).

The expression that is equivalent to \( 9x^2 - 25 \) is:

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