Prove polynomial identities and use them to solve or describe numerical relationships.
Use a polynomial identity for fast mental computation
Problem
Use a polynomial identity to evaluate \(101^2\).
Big Picture
What this problem is really about
Mental computation becomes simpler when the number is rewritten as a small adjustment from an easy benchmark. Use the square identity to separate the calculation into the benchmark square, twice the benchmark-adjustment product, and the tiny adjustment square. Estimate first so the final total can be checked against the benchmark’s size.
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