I cannot fill in the steps in this equation:
$$\Delta (A,B) = \sum_{x\in A\cup B} \vert\vert x -m_{A\cup B}\vert\vert^2 \ - \sum_{x \in A} \vert\vert x - m_{A} \vert\vert^2 - \sum_{x\in B} \vert\vert x - m_B\vert\vert^2 \\ = \frac{n_A n_B}{n_A+n_B}\vert\vert m_A-m_B\vert\vert^2$$
- $m_j$ be the center of cluster $j$
- $n_j$ be the number of points in cluster $j$
I know that it works (by calculating the solutions by hand) but I would like to see the whole transformation process.