Question

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

8 and 11.5
8 and 11.5

8.4 and 11.1
8.4 and 11.1

8 and 10
8 and 10

7.2 and 10
7.2 and 10

Answer 1

To determine which endpoints are best suited for using polynomial identities to convert differences of squares into products, we can examine the pairs provided as potential endpoints.

The difference of squares identity states that \( a^2 - b^2 = (a - b)(a + b) \).

Calculating the differences for the given pairs:

1. **8 and 11.5**:
Difference: \( 11.5 - 8 = 3.5 \)
Squares: \( (11.5)^2 - (8)^2 = 132.25 - 64 = 68.25 \)

2. **8.4 and 11.1**:
Difference: \( 11.1 - 8.4 = 2.7 \)
Squares: \( (11.1)^2 - (8.4)^2 = 123.21 - 70.56 = 52.65 \)

3. **8 and 10**:
Difference: \( 10 - 8 = 2 \)
Squares: \( (10)^2 - (8)^2 = 100 - 64 = 36 \)

4. **7.2 and 10**:
Difference: \( 10 - 7.2 = 2.8 \)
Squares: \( (10)^2 - (7.2)^2 = 100 - 51.84 = 48.16 \)

Of these options, the pair **8 and 10** has the simplest and whole number values. The calculation \( 100 - 64 = 36 \) indicates a clean application of the difference of squares identity.

Therefore, the best answer is **8 and 10**.