Formally, one can arrange the quark flavors in a $SU(n)$ fundamental representation. One can then do tensor products for flavor and spin to construct other representations like baryons and mesons. An example: $2⊗2=3⊕1$ for spin $SU(2)$ gives scalar and vector mesons, $3⊗\overline3=8⊕1$ for flavor $SU(3)$ gives the eightfold way for both scalar and vector mesons.
My question is easy: how do you get $3⊗\overline3=8⊕1$? Or for baryons: $3⊗3⊗3=10⊕8⊕8⊕1$?
