To remove brackets is to multiply the term outside the brackets by each term inside. Factorising an expression is to write it as a product of its factors. Check your understanding of the process with ...

Let 𝐾 be a number field with algebraic closure K¯, and let 𝑆 be a finite set of places of 𝐾 containing all the infinite ones. Let Γ₀ be a finitely generated subgroup of Gm(K¯), and let Γ⊂Gm(K¯) be ...