Question

Use the Distributive Property to write the expression 4x^2−36 a different way.(1 point)
Responses

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

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

C) (2x+9)(x−9)
left parenthesis 2 x plus 9 right parenthesis left parenthesis x minus 9 right parenthesis

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

Answer 1

To rewrite the expression \( 4x^2 - 36 \) using the Distributive Property, we can factor out the common factor from both terms.

Notice that both terms can be factored:
- \( 4x^2 \) can be factored as \( 4 \cdot x^2 \)
- \( -36 \) can be factored as \( -36 = -4 \cdot 9 \)

Thus, we can rewrite the expression as:
\[
4(x^2 - 9)
\]

Now we can recognize that \( x^2 - 9 \) is a difference of squares, which can be factored further:
\[
x^2 - 9 = (x - 3)(x + 3)
\]

Putting it all together, we have:
\[
4(x^2 - 9) = 4(x - 3)(x + 3)
\]

Now let's compare this with the options provided:
- A) \( (2x + 6)(2x - 6) \) is just a different representation of \( 4(x^2 - 9) \) when fully factored (as \( 4 \) can be represented by \( 2 \times 2 \)).
- B) and C) do not match.
- D) Would give a linear factorization rather than factoring the quadratic.

Among the choices, A) \( (2x + 6)(2x - 6) \) is equivalent to the original expression \( 4x^2 - 36 \).

So, the best response is:
**A) \( (2x + 6)(2x - 6) \)**.