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The following, although rather unsatisfying, does produce the desired result. term = -1 + 2 b^2 + 2 b Sqrt[b^2 - 1] Factor[Simplify[term /. b -> Cosh[z], Sinh[z] > 0] // TrigExpand] /. Sinh[z] -> Sqrt[Cosh[z]^2 - 1] /. Cosh[z] -> b (* (b + Sqrt[-1 + b^2])^2 *) Indeed, the second expression, with a LeafCount of 13, is simpler than the first,...



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