TeX source:

\begin{split} \rho_{AB} = |\psi_{AB}\rangle\langle\psi_{AB}| &= \frac{1}{2}(|0_A0_B\rangle + |1_A1_B\rangle)(\langle0_A0_B| + \langle1_A1_B|) \\ &= \frac{1}{2}(|0_A0_B\rangle\langle0_A0_B| + |0_A0_B\rangle\langle1_A1_B| + |1_A1_B\rangle\langle0_A0_B| + |1_A1_B\rangle\langle1_A1_B|). \end{split}