Use the Distributive Property to find which expression is equivalent to 9x^2 − 25.

1 answer

To factor the expression \( 9x^2 - 25 \) using the Distributive Property, we recognize it as a difference of squares. The expression can be rewritten in the form \( a^2 - b^2 \), where:

  • \( a^2 = (3x)^2 \) (since \( 9x^2 = (3x)^2 \))
  • \( b^2 = 5^2 \)

Now, we can apply the difference of squares formula, which states:

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

Substituting \( a = 3x \) and \( b = 5 \), we get:

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

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

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