Question

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

A 9x(x−25)

B (3x+5)(3x−5)

C (3x+5)2

D (4.5x+12.5)(4.5x−12.5)

Answer 1

To find which expression is equivalent to \(9x^2 - 25\) using the Distributive Property, we first recognize that the given expression is a difference of squares, which can be factored. The difference of squares formula states that \(a^2 - b^2 = (a - b)(a + b)\).

In this case, we can rewrite \(9x^2 - 25\) as follows:

- \(9x^2\) is \((3x)^2\)
- \(25\) is \(5^2\)

Thus, we can apply the difference of squares formula:

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

Looking at the provided answer choices:

A. \(9x(x - 25)\)
B. \((3x + 5)(3x - 5)\)
C. \((3x + 5)^2\)
D. \((4.5x + 12.5)(4.5x - 12.5)\)

The correct choice that is equivalent to \(9x^2 - 25\) is:

**B. \((3x + 5)(3x - 5)\)**