Using the properties of determinants and without expanding, prove that $\left|\begin{array}{lll}(b+c) & q+r & y+z \\ (c+a) & r+p & z+x \\ (a+b) & p+q & x+y\end{array}\right|=2\left|\begin{array}{lll}a & p & x \\ b & q & y \\ c & r & z\end{array}\right|$