Interpret complex polynomial/rational expressions by treating parts as single units.
Rewrite using a repeated sub-expression as u
Problem
Let \(u~=~x^2~+~1\) in \((x^2~+~1)^2~-~5(x^2~+~1)~+~6\). Rewrite the complete expression in \(u\) and factor it.
Big Picture
What this problem is really about
Substitution is useful when the same complete chunk appears in several places. Name the whole recurring parenthesis as one unit, and translate every occurrence consistently: a squared chunk becomes the square of the new variable, while an unsquared chunk becomes the variable itself. This reveals an ordinary quadratic structure without changing the original algebra.
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