A factorisation is not finished until every factor is irreducible: often the techniques must be repeated several times, recognising one special product inside another.
Example — Successive factorisations
Let us factorise :
a^8-2a^4+1 &= (a^4)^2 - 2(a^4)(1) + 1^2 \\ &= (a^4-1)^2 && \text{(quadrato di binomio)}\\ &= \bigl[(a^2+1)(a^2-1)\bigr]^2 \\ &= \boxed{(a^2+1)^2(a+1)^2(a-1)^2} \end{aligned}$$
Links
Topics: Algebraic calculus
Concepts: Difference of squares · Square of a binomial · Factorisation
Skills: Factorising