Prove polynomial identities and use them to solve or describe numerical relationships.
Factor a polynomial by recognizing a special identity
Problem
Factor \(x^2~-~25\) completely using an identity.
Big Picture
What this problem is really about
Before factoring, name the structure: two perfect squares separated by subtraction. Take the square root of each term and place those roots in conjugate factors, one with subtraction and one with addition. Multiplying back is a quick check because the opposite cross terms should cancel and reproduce the original expression.
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