To determine which expression is equivalent to \(9x^2 - 25\) using the Distributive Property (also known as the FOIL method for binomials), we can identify that \(9x^2 - 25\) is a difference of squares, which can be factored as follows:
\[ a^2 - b^2 = (a + b)(a - b) \]
In this case, we have:
\[ a = 3x \quad \text{and} \quad b = 5 \]
So:
\[ 9x^2 - 25 = (3x)^2 - 5^2 = (3x + 5)(3x - 5) \]
Now let's look at the provided options:
- \((3x + 5)(3x - 5) \) - This is equivalent to \(9x^2 - 25\).
- \(9x(x - 25)\) - This expands to \(9x^2 - 225x\), which is not equivalent to \(9x^2 - 25\).
- \((3x + 5)^2\) - This expands to \(9x^2 + 30x + 25\), which is not equivalent to \(9x^2 - 25\).
- \((4.5x + 12.5)(4.5x - 12.5)\) - This does not relate to \(9x^2 - 25\) and expands differently.
Therefore, the correct expression equivalent to \(9x^2 - 25\) is:
\((3x + 5)(3x - 5)\)
1 answer