This determinant is called "Vandermonde determinant" = ABCD (b-a) (c-a) (d-a) ((c-b) (d-b) (d-c).

Process: Using the properties of determinant, the fourth row-the third row× a, the third row-the second row× a, the second row-the first row× a,

The element in the first column of the second to fourth rows is 0. Using the expansion property of determinant,

The original determinant is equal to 1(b-a)(c-a)(d-a)* (a third-order Vandermonde determinant composed of b, c, d, c and d). Therefore, the above results can be obtained.