这种对称矩阵行列式有没什么简便的做法啊？

1 3 5 7
3 5 7 1 c1+c2
5 7 1 3 c1+c3
7 1 3 5 c1+c4

=
15 3 5 7
15 5 7 1
15 7 1 3
15 1 3 5

=15
1 3 5 7
1 5 7 1 r2-r1
1 7 1 3 r3-r1
1 1 3 5 r4-r1

=15
1 3 5 7
0 2 2 -6
0 4 -4 -4
0 -2 -2 -2

=15*2*4*(-2)
1 3 5 7
0 1 1 -3
0 1 -1 -1 r3-r2
0 1 1 1 r4-r2

=-240
1 3 5 7
0 1 1 -3
0 0 -2 2
0 0 0 4
=-240*1*1*(-2)*4
=1920