Use the Distributive Property to find which expression is equivalent to 9x2−25

Question

.(1 point)
Responses

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

(3x+5)(3x−5)
left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis

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

(4.5x+12.5)(4.5x−12.5)

Answer 1

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

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

In the given expression:

• \( 9x^2 \) can be rewritten as \( (3x)^2 \)
• \( 25 \) can be rewritten as \( 5^2 \)

Thus, we can apply the difference of squares formula: \[ 9x^2 - 25 = (3x)^2 - 5^2 = (3x - 5)(3x + 5) \]

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

So, the correct response is: \[ (3x + 5)(3x - 5) \]