Question

Use the Distributive Property to find which expression is equivalent to 9x2−25 .
a. (3x+5)(3x−5) left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis
b. 9x(x−25) 9 x left parenthesis x minus 25 right parenthesis
c. (3x+5)2 left parenthesis 3 x plus 5 right parenthesis squared
d. (4.5x+12.5)(4.5x−12.5)

Answer 1

To find which expression is equivalent to \( 9x^2 - 25 \), we can recognize that it is a difference of squares, which follows the formula:

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

Here, we can identify:
- \( a = 3x \) (since \( (3x)^2 = 9x^2 \))
- \( b = 5 \) (since \( 5^2 = 25 \))

Applying the difference of squares formula:

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

Now, let's compare this result to the given options:

a. \( (3x + 5)(3x - 5) \) (This matches our result)

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

c. \( (3x + 5)^2 \) (This does not match)

d. \( (4.5x + 12.5)(4.5x - 12.5) \) (This does not match)

Thus, the correct choice is:

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