shortcut method for calculating a determinant \begin{vmatrix} b+c & a & a \\ b & c+a & b \\ c & c& a+b \end{vmatrix} = 4abc
Is there any shortcut method to compute this determinant without breaking by definition. Need some help please.

$$\begin{vmatrix}
b+c & a & a \\ b & c+a & b \\ c & c& a+b 
\end{vmatrix} \xrightarrow{-R_1+R_2} \begin{vmatrix}
b+c & a & a \\ -c & c & -a+b \\ c & c& a+b 
\end{vmatrix} \xrightarrow{-R_2+R_3} \begin{vmatrix}
b+c & a & a \\ -c & c & -a+b \\ 2c & 0 & 2a 
\end{vmatrix} \xrightarrow{-0.5R_3+R_1} \begin{vmatrix}
b & a & 0 \\ -c & c & -a+b \\ 2c & 0 & 2a 
\end{vmatrix} \xrightarrow{-0.5R_3+R_2}  \begin{vmatrix}
b & a & 0 \\ 0 & c & b \\ 2c & 0 & 2a 
\end{vmatrix} = b(2ac) - a (-2bc) = 4abc$$
