$$\det \begin{pmatrix} 0&x_1&x_2&\ldots&x_n\\ x_1&a_{11}&a_{12}&\ldots&a_{1n}\\ x_2&a_{21}&a_{22}&\ldots&a_{2n}\\ \ldots&\ldots&\ldots&\ldots&\ldots\\ x_n&a_{n1}&a_{n2}&\ldots&a_{nn}\\ \end{pmatrix} = -\sum_{i=1}^n \sum_{j=1}^n A_{ij}x_ix_j.$$
where $A_{ij}\ \text{is the cofactor of }\ a_{ij}\ \text {and}\ n>1.$
My question is proving this problem.
First, I tried to take the cofactor expansion along the first row.
But I don't know what I do next.
Please give me some hints for proving this problem