Question

Match the difference of squares with its factored form. NOT ALL ANSWER CHOICES WILL BE USED. Reference Sheet - Difference of Two Squares (3 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 4x2−36 4 𝑥 2 − 36 x2−36 𝑥 2 − 36 36x2−4 36 𝑥 2 − 4 (18x+2)(18x−2) ( 18 𝑥 + 2 ) ( 18 𝑥 − 2 ) (2x+18)(2x−18) ( 2 𝑥 + 18 ) ( 2 𝑥 − 18 ) (2x+6)(2x−6) ( 2 𝑥 + 6 ) ( 2 𝑥 − 6 ) (6x+2)(6x−2) ( 6 𝑥 + 2 ) ( 6 𝑥 − 2 ) (x+18)(x−18) ( 𝑥 + 18 ) ( 𝑥 − 18 ) (x+6)(x−6) ( 𝑥 + 6 ) ( 𝑥 − 6 )

Answer 1

To match the difference of squares with its factored form, we first identify the expressions we have and then factor them accordingly.

1. **4x² - 36**:
This can be rewritten as:
\[
4x² - 6²
\]
Using the difference of squares formula \(a² - b² = (a - b)(a + b)\), we factor this as:
\[
(2x - 6)(2x + 6)
\]
However, the simplified form would be:
\[
2(x - 3)(x + 3)
\]
Thus, from the options provided, it matches best with:
(2x + 6)(2x - 6)

2. **x² - 36**:
This can be rewritten as:
\[
x² - 6²
\]
Applying the difference of squares formula:
\[
(x - 6)(x + 6)
\]
This matches:
(x + 6)(x - 6)

3. **36x² - 4**:
This can be rewritten as:
\[
(6x)² - 2²
\]
Using the difference of squares formula:
\[
(6x - 2)(6x + 2)
\]
So, this matches with:
(6x + 2)(6x - 2)

Therefore, the correct factorizations are:
- **4x² - 36**: (2x + 6)(2x - 6)
- **x² - 36**: (x + 6)(x - 6)
- **36x² - 4**: (6x + 2)(6x - 2)

Thus, the responses match as follows:
1. \(4x² - 36\) -> (2x + 6)(2x - 6)
2. \(x² - 36\) -> (x + 6)(x - 6)
3. \(36x² - 4\) -> (6x + 2)(6x - 2)

You can fill in the inputs as per the matches provided.