To determine which pair of endpoints is best suited for using polynomial identities (specifically the difference of squares identity) to convert differences of numerical squares into products, we need to consider the mathematical structure of the endpoints.
The difference of squares identity states: \[ a^2 - b^2 = (a - b)(a + b) \]
We want pairs of numbers (endpoints) where the difference between their squares can be easily expressed using this identity.
Let's analyze the pairs you provided:
-
0 and 7.2:
- \( 7.2^2 - 0^2 = 7.2^2 = 51.84 \)
- Difference of squares not applicable (just gives a single value).
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0 and 8 and 11.5:
- \( 11.5^2 - 0^2 = 11.5^2 = 132.25 \)
-
0 and 8.4 and 11.1:
- \( 11.1^2 - 8.4^2 \)
- The difference is \( (11.1 - 8.4)(11.1 + 8.4) \).
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0 and 8 and 10:
- \( 10^2 - 8^2 = (10 - 8)(10 + 8) = 2 \times 18 = 36 \).
From this analysis, the best option for using the difference of squares identity would be the pair that allows us to apply the identity clearly.
Thus, the best candidates are "8 and 10", as this pair allows for a direct application of the difference of squares identity.
If you have further questions, feel free to ask!
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