A factorisation often requires two techniques in sequence: first a common factor is collected, then a difference of squares is recognised in the remaining factor.
Example — Collecting and difference of squares
Let us factorise :
9b^2 - a^2 b^2 &= b^2(9-a^2) && \text{(fattor comune } b^2\text{)}\\ &= b^2(3+a)(3-a) && \text{(differenza di quadrati)}\\ &= \boxed{b^2(3+a)(3-a)} \end{aligned}$$
Links
Topics: Algebraic calculus
Concepts: Difference of squares · Collecting a common factor · Factorisation
Methods: Special products · Common factoring
Skills: Factorising