Prove polynomial identities and use them to solve or describe numerical relationships.
Identify which polynomial identity matches a given expression
Problem
Identify the polynomial identity represented by \(x^2~-~36\).
Big Picture
What this problem is really about
Classify an identity by its structure rather than by a memorized name alone. Count the terms, rewrite each term as an exact power, and note the operation connecting them. Two squared quantities separated by subtraction belong to a different family from three-term square patterns or two-term cube patterns, and a quick factorization can confirm the classification.
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