Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.2 - Factoring the Difference of Two Squares - Problem Set 6.2 - Page 248: 42

$(x^2+1)(x+1)(x-1)$

Using $a^2-b^2=(a+b)(a-b)$, the factored form of the given expression, $ x^4-1 ,$ is \begin{array}{l}\require{cancel} (x^2+1)(x^2-1) .\end{array} Since the second factor is still a difference of $2$ squares, using the same factoring technique, the completely factored form of the expression above is \begin{array}{l}\require{cancel} (x^2+1)(x+1)(x-1) .\end{array}