Question

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

(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

(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

Answer 1

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

The difference of squares can be factored using the formula:
\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, we can identify:
- \(a = 3x\) (because \((3x)^2 = 9x^2\))
- \(b = 5\) (because \(5^2 = 25\))

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

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

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