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

Question

Responses

(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)
left parenthesis 4.5 x plus 12.5 right parenthesis left parenthesis 4.5 x minus 12.5 right parenthesis

9x(x−25)

Answer 1

To identify which expression is equivalent to \(9x^2 - 25\) using the Distributive Property, we can first recognize that \(9x^2 - 25\) is a difference of squares. This can be factored as follows:

The expression follows the form \(a^2 - b^2\), where:

• \(a = 3x\)
• \(b = 5\)

Using the difference of squares formula, \(a^2 - b^2 = (a - b)(a + b)\), we can rewrite \(9x^2 - 25\) as:

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

Now, let’s compare this with the given options:

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

From the analysis, we see that the first option, \((3x + 5)(3x - 5)\), represents the correct factorization of \(9x^2 - 25\).

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

\(\boxed{(3x + 5)(3x - 5)}\)