Question

Which of the following endpoints is best suited for using polynomial identities to convert differences of numerical squares into products?(1 point)
Responses

7.2 and 10
7.2 and 10

8 and 11.5
8 and 11.5

8 and 10
8 and 10

8.4 and 11.1

Answer 1

To determine which endpoints are best suited for using polynomial identities to convert differences of numerical squares into products, you can use the difference of squares formula, which states:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, you are looking for pairs of numbers where one is the square of a number and the other can be expressed as such, or where their difference can yield a product form.

Let's analyze the given pairs:

1. **7.2 and 10**:
- \(10^2 - 7.2^2 = 100 - 51.84 = 48.16 \)
- Not a perfect square difference, so this pair is not well-suited for this identity.

2. **8 and 11.5**:
- \(11.5^2 - 8^2 = 132.25 - 64 = 68.25\)
- Not a perfect square difference, so this pair is not well-suited.

3. **8 and 10**:
- \(10^2 - 8^2 = 100 - 64 = 36\)
- This is a perfect square difference, and can be converted to
\((10 - 8)(10 + 8) = 2 \times 18 = 36\). This pair is well-suited.

4. **8.4 and 11.1**:
- \(11.1^2 - 8.4^2 = 123.21 - 70.56 = 52.65\)
- Not a perfect square difference, so this pair is not suitable.

Among these options, the best suited pair for using polynomial identities to convert differences of numerical squares into products is:

**8 and 10**.