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:
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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.
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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.
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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.
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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.