Question

Use the Distributive Property to write the expression 4x2−36
a different way.(1 point)
Responses

4x(x−9)
4 x left parenthesis x minus 9 right parenthesis

(2x+6)(2x−6)
left parenthesis 2 x plus 6 right parenthesis left parenthesis 2 x minus 6 right parenthesis

(x+18)(x−18)
left parenthesis x plus 18 right parenthesis left parenthesis x minus 18 right parenthesis

(2x+9)(x−9)

Answer 1

To rewrite the expression \(4x^2 - 36\) using the Distributive Property, we can factor it. We notice that this expression is a difference of squares and also can take out the common factor:

1. First, factor out the greatest common factor from both terms. The greatest common factor here is 4:
\[
4(x^2 - 9)
\]

2. Next, recognize that \(x^2 - 9\) is a difference of squares, which can be factored as:
\[
(x + 3)(x - 3)
\]

3. Combining these, we rewrite the entire expression:
\[
4(x + 3)(x - 3)
\]

However, this specific representation doesn't match any of the options you provided.

Among the options listed, the one that most closely relates to the correct factorization of \(4x^2 - 36\) is:

**Response:**
\[
(2x + 6)(2x - 6)
\]
Which factors as:
\[
4(x^2 - 9)
\]
And simplifies back to \(4x^2 - 36\).

So the correct response is:
\((2x + 6)(2x - 6)\) (left parenthesis 2 x plus 6 right parenthesis left parenthesis 2 x minus 6 right parenthesis).