To convert differences of numerical squares into products using polynomial identities, you can apply the identity \( a^2 - b^2 = (a - b)(a + b) \).
Given the pairs of numbers you mentioned, let's evaluate the differences of their squares:
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8 and 10: \[ 10^2 - 8^2 = (10 - 8)(10 + 8) = 2 \cdot 18 = 36 \]
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8.4 and 11.1: \[ 11.1^2 - 8.4^2 = (11.1 - 8.4)(11.1 + 8.4) = 2.7 \cdot 19.5 = 52.65 \]
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8 and 11.5: \[ 11.5^2 - 8^2 = (11.5 - 8)(11.5 + 8) = 3.5 \cdot 19.5 = 68.25 \]
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7.2 and 10: \[ 10^2 - 7.2^2 = (10 - 7.2)(10 + 7.2) = 2.8 \cdot 17.2 = 48.16 \]
The identity can be used effectively on all pairs to find the numerical differences and product combinations, but the choice of which endpoint is best depends on the context (like the specific application of the identities). However, for purely evaluating numbers, any of the endpoints allows polynomial manipulation; just choose the pair that yields the calculation that you wish to evaluate further.
If you need to establish which one fits best based on some specific criteria, please provide that context. Otherwise, all pairs can work, but more context would clarify the best endpoint in an application.
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