Question

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

Answer 1

To use the Distributive Property to find an equivalent expression for \(9x^2 - 25\), we recognize that the expression can be factored as a difference of squares.

The difference of squares formula is:

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

In the expression \(9x^2 - 25\), we can identify \(a^2 = 9x^2\) and \(b^2 = 25\).

Thus, we have:
- \(a = 3x\) (since \((3x)^2 = 9x^2\))
- \(b = 5\) (since \(5^2 = 25\))

Applying the difference of squares formula, we get:

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

Now let's check the original response, which seems to imply we should consider the provided options.

If you provided \( (4.5x + 12.5)(4.5x - 12.5) \), let's see if that would simplify to match our expression.

By expanding that:

\[
(4.5x + 12.5)(4.5x - 12.5) = (4.5x)^2 - (12.5)^2 = 20.25x^2 - 156.25
\]

This does not match \(9x^2 - 25\).

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

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

If that option is not in the responses you provided, then none of the options given is the correct equivalent expression.