Question

Use the Distributive Property to write the expression 4x2−36 a different way.(1 point) Responses (2x+6)(2x−6) left parenthesis 2 x plus 6 right parenthesis left parenthesis 2 x minus 6 right parenthesis (2x+9)(x−9) left parenthesis 2 x plus 9 right parenthesis left parenthesis x minus 9 right parenthesis 4x(x−9) 4 x left parenthesis x minus 9 right parenthesis (x+18)(x−18)

Answer 1

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

1. Notice that \(4x^2 - 36\) can be factored as a difference of squares.
2. We can express it as \(4(x^2 - 9)\).
3. Next, recognize that \(x^2 - 9\) is a difference of squares, which factors to \((x + 3)(x - 3)\).

So, \(4x^2 - 36 = 4(x^2 - 9) = 4(x + 3)(x - 3)\).

Going back to the original expression, we can also factor it in terms of the form \( (2x + 6)(2x - 6) \). To see why, observe:

1. Recognize that \(4x^2 - 36\) can also be expressed as \( (2x)^2 - 6^2\), which is again a difference of squares.
2. Thus, \(4x^2 - 36 = (2x + 6)(2x - 6)\).

Among the options you provided, the response that correctly utilizes the Distributive Property to rewrite the expression \(4x^2 - 36\) would be:

**(2x + 6)(2x - 6)**.