Solve this following

Using properties of determinants prove that:

$\left|\begin{array}{lll}1 & b+c & b^{2}+c^{2} \\ 1 & c+a & c^{2}+a^{2} \\ 1 & a+b & a^{2}+b^{2}\end{array}\right|=(a-b)(b-c)(c-a)$