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)

Answer 1

To find which expression is equivalent to \( 9x^2 - 25 \), we can observe that \( 9x^2 - 25 \) fits the form of a difference of squares, which is given by the formula \( a^2 - b^2 = (a + b)(a - b) \).

In this case:

• \( a^2 = 9x^2 \) implies \( a = 3x \),
• \( b^2 = 25 \) implies \( b = 5 \).

Now, applying the difference of squares formula:

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

Thus, the expression equivalent to \( 9x^2 - 25 \) is:

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

So the correct response is:

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