It has been asked before if it holds that $B\otimes (C\oplus D)\cong (B\otimes C)\oplus (B\otimes D)$, for B,C,D all being real vector spaces.
Is it known if the analogous statement, $(B\otimes C)\oplus D\cong (B\oplus D)\otimes (C\oplus D)$, is true?
Are there any good counterexamples? Are there specific conditions under which this is true?