Use the Distributive Property to find which expression is equivalent to 9x^2−25 .(1 point)

Question

Responses

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

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

(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 this expression is a difference of squares. The difference of squares formula states that:

\[ a^2 - b^2 = (a - b)(a + b) \]

In the given expression \( 9x^2 - 25 \), we can identify:

• \( a^2 = 9x^2 \) so \( a = 3x \)
• \( b^2 = 25 \) so \( b = 5 \)

Now we can apply the difference of squares formula:

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

Looking at the options provided, we see that the expression equivalent to \( 9x^2 - 25 \) is:

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

So the correct response is:

(3x+5)(3x−5)