In these notes on (co)homology of algebras, Kassel claims (page 14) that the Hochschild standard resolution of a $k$-algebra $A$, with group of $q$-chains equals $$C'_q(A):= A \otimes A^{\otimes q} \otimes A$$ is a resolution of $A$ by free $A$-bimodules.
Question. Why is $C'_q(A)$ free as $A$-bimodule? In this question Mariano Suárez-Álvarez explains that if $A$ is projective as $k$-module, then $C'_q(A)$ is projective as $A$-bimodule, but the claim in Kassel's notes stronger (he does not take any assumption on $A$).