\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}
T_{pq} = T_{ij} & = & \frac{q_j}{r^3} \left[ 1 - 
  3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p_i}\times\vec{r}) \\
T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} \left[ 1 -
  3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p_j}\times\vec{r}) \\
T_{pp} = T_{ij} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \times \vec{p_j}) + \\
  & & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_j}\bullet\vec{r})
  (\vec{p_i} \times \vec{r}) \\
T_{pp} = T_{ji} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p_j} \times \vec{p_i}) + \\
  & & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \bullet \vec{r}) 
  (\vec{p_j} \times \vec{r}) \\
\end{eqnarray*}                           

\end{document}