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2 $begingroup$ Let $ X $ be an Banach algebra (not necessarily commutative), and let $ x, y, z in X $ . Suppose that $ | x - y | < M $ . I want to bound $ | zx - yz | $ in terms of $ M $ by writing $ zx - yz $ as a product of terms including the term $ x - y $ , but I don't see how to do so (or if it is even possible). If it is possible, I am assuming it is just an elementary factoring trick that I am blanking out on. Any help would be appreciated. Thanks! functional-analysis banach-algebras share | cite | improve this question edited Jan 21 at 18:39 LMW