Question
Use the Distributive Property to write the expression 4x2−36 a different way.
(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
4x(x−9)
4 x left parenthesis x minus 9 right parenthesis
(2x+9)(x−9)
(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
4x(x−9)
4 x left parenthesis x minus 9 right parenthesis
(2x+9)(x−9)
Answers
Answered by
GPT-4o mini
To use the Distributive Property (also known as factoring) on the expression \(4x^2 - 36\), we first recognize that this expression is a difference of squares. The expression can be rewritten and factored as follows:
1. Factor out the common term. Notice that \(4\) can be factored out from both terms:
\[
4(x^2 - 9)
\]
2. Now, recognize that \(x^2 - 9\) is a difference of squares, which can be factored further:
\[
4(x + 3)(x - 3)
\]
Thus, the expression \(4x^2 - 36\) can be rewritten as \(4(x + 3)(x - 3)\).
However, if you were looking for another form from the options provided in your question, let's analyze the options:
1. **(2x + 6)(2x - 6)** - This expands to \(4x^2 - 36\).
2. **(x + 18)(x - 18)** - This expands to \(x^2 - 324\).
3. **4x(x - 9)** - This expands to \(4x^2 - 36x\).
4. **(2x + 9)(x - 9)** - This expands to \(2x^2 - 18x + 9x - 81\) or \(2x^2 - 9x - 81\).
The correct option that rewrites the expression \(4x^2 - 36\) is:
\[
(2x + 6)(2x - 6)
\]
This expression is equivalent to the original \(4x^2 - 36\) when expanded.
1. Factor out the common term. Notice that \(4\) can be factored out from both terms:
\[
4(x^2 - 9)
\]
2. Now, recognize that \(x^2 - 9\) is a difference of squares, which can be factored further:
\[
4(x + 3)(x - 3)
\]
Thus, the expression \(4x^2 - 36\) can be rewritten as \(4(x + 3)(x - 3)\).
However, if you were looking for another form from the options provided in your question, let's analyze the options:
1. **(2x + 6)(2x - 6)** - This expands to \(4x^2 - 36\).
2. **(x + 18)(x - 18)** - This expands to \(x^2 - 324\).
3. **4x(x - 9)** - This expands to \(4x^2 - 36x\).
4. **(2x + 9)(x - 9)** - This expands to \(2x^2 - 18x + 9x - 81\) or \(2x^2 - 9x - 81\).
The correct option that rewrites the expression \(4x^2 - 36\) is:
\[
(2x + 6)(2x - 6)
\]
This expression is equivalent to the original \(4x^2 - 36\) when expanded.