Formula_23012

\[\begin{gathered}\left(a_{1}, \ldots, a_{n}, b_{1}, \ldots, b_{n}, c\right)\left(a_{1}^{\prime}, \ldots, a_{n}^{\prime}, b_{1}^{\prime}, \ldots, b_{n}^{\prime}, c^{\prime}\right)= \\=\left(a_{1}+a_{1}^{\prime}, \ldots, a_{n}+a_{n}^{\prime}, b_{1}+b_{1}^{\prime}, \ldots, b_{n}+b_{n}^{\prime}, c+c^{\prime}+\sum a_{i} b_{i}^{\prime}\right) .\end{gathered}\]