> [!NOTE] Definition (Product of univariate polynomial forms) > Let $f,g\in R[x]$ be [[Ring of Polynomial Forms|polynomials]] over $R$ in $x.$ Let $f=\sum_{j=0}^{m}a_{j}x^{j}$and $g=\sum_{k=0}^{n}b_{k}x^{k}$Then the product of $f$ and $g$ is defined as $fg = \sum_{l=0}^{m+n} c_{l} x^{l}$where $c_{l}=\sum_{j+k=l}a_{j}b_{k}$