Use the distributive property to find which expression is equivalent to 9x²-25.

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

1 answer

To use the distributive property to factor the expression \(9x^2 - 25\), we can recognize that it is a difference of squares. The general form for factoring a difference of squares \(a^2 - b^2\) is \((a + b)(a - b)\).

In this case:

  • \(9x^2\) can be expressed as \((3x)^2\).
  • \(25\) can be expressed as \(5^2\).

Therefore, we can rewrite \(9x^2 - 25\) as: \[ (3x)^2 - 5^2 \]

Applying the difference of squares formula, we get: \[ (3x + 5)(3x - 5) \]

Now, let's compare this result with the answer choices provided:

A. \((3x+5)(3x-5)\) - This matches our factored expression.

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

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

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

The expression that is equivalent to \(9x^2 - 25\) is: A. \((3x+5)(3x-5)\).