Calculate det(A)\det(A)det(A) for A=(1aa21bb21cc2)A = \begin{pmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{pmatrix}A=111abca2b2c2.
(b−a)(c−a)(c−b)(b-a)(c-a)(c-b)(b−a)(c−a)(c−b)
(a−b)(b−c)(c−a)(a-b)(b-c)(c-a)(a−b)(b−c)(c−a)
abcabcabc
a+b+ca+b+ca+b+c