Question

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 parenthesis

(3x+5)2
left parenthesis 3 x plus 5 right parenthesis squared

(3x+5)(3x−5)
left parenthesis 3 x plus 5 right parenthesis left parenthesis 3 x minus 5 right parenthesis

9x(x−25)

Answer 1

To determine which expression is equivalent to \(9x^2 - 25\), we can recognize that this expression is a difference of squares. The difference of squares can be factored using the formula:

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

Here \(a^2\) is \(9x^2\) and \(b^2\) is \(25\).

1. Identify \(a\) and \(b\):
   • \(a = 3x\) (since \( (3x)^2 = 9x^2 \))
   • \(b = 5\) (since \(5^2 = 25\))

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

Now we can evaluate the choices provided:

1. (4.5x + 12.5)(4.5x - 12.5): This does not match our expression.
2. (3x + 5)^2: This is a perfect square, not a difference of squares.
3. (3x + 5)(3x - 5): This matches our earlier conclusion: \(9x^2 - 25\) can be factored as this.
4. 9x(x - 25): This does not represent the original expression correctly.

Thus, the equivalent expression is:

(3x + 5)(3x - 5).