Question

Use the Distributive Property to write the expression $4x^{2}-36$ a different way.
(1 point)
$(x+18)(x-18)$
$(2x+6)(2x-6)$
$4x(x-9)$
$(2x+9)(x-9)$

Answer 1

To use the Distributive Property to write the expression \( 4x^2 - 36 \) in a different way, we can factor it.

First, recognize that \( 4x^2 - 36 \) is a difference of squares:

\[
4x^2 - 36 = (2x)^2 - 6^2
\]

Using the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), we set \( a = 2x \) and \( b = 6 \):

\[
4x^2 - 36 = (2x - 6)(2x + 6)
\]

This expression is equivalent to \( 4x^2 - 36 \) but is written in a different way.

Among the options provided, \( (2x+6)(2x-6) \) correctly represents the expression \( 4x^2 - 36 \). Therefore, the correct answer is:

\[
\boxed{(2x+6)(2x-6)}
\]