This is LaTeX code:

[latex]
= \left( {p_1 p} \right)^{n_1 + 1} + \left( {p_1 p} \right)^{n_2 + 1} - p^2 p_2 \left( {p_1 p} \right)^{n_1 + n_2 } \left( {2p_1 - 1} \right)
[/latex]