Tensor product decompositions for su(3) of an irreducible representation with itself and with its conjugate

In this article a method to obtain the decomposition, including multiplicities, of an su(3) irreducible representation with itself and with its conjugate, is provided. The decomposition of such tensor products plays an important role in physics. The objective is to provide a simple method for performing these decompositions in addition to showing how this method can be used to derive several interesting facts about the decompositions, particularly in regards to multiplicities.