A little diversion

It probably isn't obvious why we can get away with only one $D$ for all of the gamete frequencies. The short answer is:

There are four gametes. That means we need three parameters to describe the four frequencies. $p_1$ and $p_2$ are two. $D$ is the third.

Another way is to do a little algebra to verify that the definition is self-consistent.

$$\begin{eqnarray*} D &=& x_{11}x_{22} - x_{12}x_{21} \\ &=& (p_1p_2 + D)(q_1q... ..._1(q_2 + p_2)\right) \\ &=& D(p_1 + q_1) \\ &=& D \quad. \end{eqnarray*}$$