use the distributive property to find which expression is equivalent to 9x^2 - 25

1 answer

To use the distributive property and find an equivalent expression for \(9x^2 - 25\), we can factor the expression, as it represents a difference of squares.

The expression \(9x^2 - 25\) can be rewritten using the fact that \(9x^2\) is \((3x)^2\) and \(25\) is \(5^2\). This allows us to apply the difference of squares formula, which is:

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

In this case, let:

  • \(a = 3x\)
  • \(b = 5\)

Applying the difference of squares formula, we have:

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

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

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