Calculate complex determinant $$\left| {\begin{array}{*{20}{c}}{{a^2}}&{{{(a + 1)}^2}}&{{{(a + 2)}^2}}&{{{(a + 3)}^2}}\\{{b^2}}&{{{(b + 1)}^2}}&{{{(b + 2)}^2}}&{{{(b + 3)}^2}}\\{{c^2}}&{{{(c + 1)}^2}}&{{{(c + 2)}^2}}&{{{(c + 3)}^2}}\\{{d^2}}&{{{(d + 1)}^2}}&{{{(d + 2)}^2}}&{{{(d + 3)}^2}}\end{array}} \right|
$$
It's very stupid desicion for me to expand it by row or column. 
Any suggestions?

By the fourth column (resp. the third column, the second column) subtract the third column (resp. the second column, the first column), you get 
$\left|\begin{array}{cccc} 
a^2 & 2a+1 & 2a+3 & 2a+5 \\
b^2 & 2b+1 & 2b+3 & 2b+5 \\
c^2 & 2c+1 & 2c+3 & 2c+5 \\
d^2 & 2d+1 & 2d+3 & 2d+5 \\
\end{array} \right|=0$
