Use expression structure to identify useful rewrites, such as difference-of-squares factoring.
Factor using a repeated subexpression
Problem
Factor \((x+1)^{2}-25\) completely in \(x\). First treat \(x+1\) as one quantity, apply the difference-of-squares pattern, then simplify both factors and verify their product.
Big Picture
What this problem is really about
Treating the repeated binomial as one temporary quantity exposes a difference-of-squares pattern. We’ll factor in that temporary variable, substitute the complete original binomial back into both conjugate factors, simplify each factor separately, and expand both forms to verify the result remains entirely in x.
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