Compute the determinant The following problem is taken from here exercise $2:$

Question: Evaluate the determinant: 
  \begin{vmatrix}
0 & x & x & \dots & x \\
y & 0 & x & \dots & x \\
y & y & 0 & \dots & x \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
y & y & y & \dots & 0
\end{vmatrix}

My attempt: 
I tried to use first row substract second row to obtain 
\begin{pmatrix}
y & -x & 0 \dots & 0
\end{pmatrix}
and also first row subtracts remaining rows. 
However, I have no idea how to proceed. 

Chappers's expanding is correct, but the answer is imho wrong: it is not correct for $n=2$. Iterating over $\Delta$ gives you
$$
\Delta_n = (-1)^{n-1}xy\frac{x^{n-1}-y^{n-1}}{x-y}
$$
