Question

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

To determine which expression is equivalent to \(9x^2 - 25\), we can recognize that this expression is a difference of squares. The difference of squares formula is given by:

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

In the expression \(9x^2 - 25\), we can identify:
- \(a^2 = 9x^2\) (where \(a = 3x\))
- \(b^2 = 25\) (where \(b = 5\))

Using the difference of squares formula, we can factor \(9x^2 - 25\) as follows:

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

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

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

So, the correct response is:

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