A determinant

\[\left|\matrix{x&a&a&\cdots&a\\b&x&a&\cdots&a\\b&b&x&\cdots&a\\\vdots&\vdots&\vdots&\ddots&\vdots\\b&b&b&\cdots&x}\right| \]

\[=x\sum_{i=0}^{n-1}\left((x-a)^i(x-b)^{n-1-i}\right)-(x-a)(x-b)\sum_{i=0}^{n-2}(x-a)^i(x-b)^{n-2-i} \]