Using properties of determinants, prove the following `|(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta)|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)`

Explanation

To prove the determinant equality

\[
\left|
\begin{array}{ccc}
\alpha & \beta & \gamma \\
\alpha^2 & \beta^2 & \gamma^2 \\
\beta + \gamma & \gamma + \alpha & \alpha + \beta
...