TeX source:

\begin{split} &(\mathbf{M}_{+A}\otimes\mathbf{I}_B)\left( \dfrac{1}{2}|0\rangle\langle0|_A\otimes|0\rangle\langle0|_B + \dfrac{1}{2}|1\rangle\langle1|_A\otimes|1\rangle\langle1|_B \right)(\mathbf{M}_{+A}\otimes\mathbf{I}_B) \\ &= \dfrac{1}{2}\left\{ |+\rangle\langle+|_A|0\rangle\langle0|_A|+\rangle\langle+|_A\otimes|0\rangle\langle0|_B + |+\rangle\langle+|_A|1\rangle\langle1|_A|+\rangle\langle+|_A\otimes|1\rangle\langle1|_B \right\} \\ &= \dfrac{1}{4}\left\{|+\rangle\langle+|_A\otimes|0\rangle\langle0|_B + |+\rangle\langle+|_A\otimes|1\rangle\langle1|_B \right\}. \end{split}