Use the Distributive Property to write the expression 4x2−36

Question

a different way.(1 point)
Responses

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

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

Answer 1

To apply the Distributive Property to the expression \(4x^2 - 36\), we can first factor out the greatest common factor (GCF) from the expression.

We notice that both terms have \(4\) as a common factor:

\[ 4(x^2 - 9) \]

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

So, the complete factorization of the expression is:

\[ 4(x + 3)(x - 3) \]

However, since your options do not match this exactly, the most relevant choice would be to factor out \(4\) and leave it in the form \(4(x - 9)\), which is not a complete factorization but is very close to one of your options.

The best rephrasing using the options given is:

4(x - 9) (but noted it doesn't reflect factoring completely).

The other answer (2x + 6)(2x - 6) could also be correct initially since \(4x^2 - 36 = (2x)^2 - 6^2\) which is a difference of squares as well.

So the closest expression using complete factorization correctly aligned is:

\[ (2x + 6)(2x - 6) \]

Please inform me if you need further clarification!