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

Question

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

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

Answer 1

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

The formula for the difference of squares is: \[ a^2 - b^2 = (a-b)(a+b) \]

In this case, we can rewrite \( 9x^2 - 25 \) as: \[ (3x)^2 - (5)^2 \] Here, \( a = 3x \) and \( b = 5 \).

Applying the difference of squares formula: \[ (3x - 5)(3x + 5) \]

Now let's match this result with the provided responses:

1. \((3x + 5)^2\)
2. \((3x + 5)(3x - 5)\) (This matches!)
3. \(9x(x - 25)\)
4. \((4.5x + 12.5)(4.5x - 12.5)\)

Thus, the expression equivalent to \( 9x^2 - 25 \) is: \[ \boxed{(3x + 5)(3x - 5)} \]