$\left|\begin{array}{ccc}3& \mathrm{a}+ \mathrm{b}+ \mathrm{c}& {\mathrm{a}}^2 + {\mathrm{b}}^2 + {\mathrm{c}}^2\\ \mathrm{a} + \mathrm{b}+ \mathrm{c}& {\mathrm{a}}^2 + {\mathrm{b}}^2 + {\mathrm{c}}^2& {\mathrm{a}}^3 + {\mathrm{b}}^3 + {\mathrm{c}}^3\\ {\mathrm{a}}^2 + {\mathrm{b}}^2 + {\mathrm{c}}^2& {\mathrm{a}}^3 + {\mathrm{b}}^3 + {\mathrm{c}}^3& {\mathrm{a}}^4 + {\mathrm{b}}^4 + {\mathrm{c}}^4\end{array}\right| = \mathrm{k}{(\mathrm{a}-\mathrm{b})}^2{(\mathrm{b}-\mathrm{c})}^2{(\mathrm{c}-\mathrm{a})}^2$then k =