You can be completely explicit in this matter. For $T_j$ in a commutative algebra
$$
T_1T_2\dots T_k=\frac{1}{2^k k!}\sum_{\epsilon_j=\pm 1} \epsilon_1\dots\epsilon_k(\epsilon_1T_1
+\dots+\varepsilon_{k}T_{k})^k.
$$
The following lemma in available in the Euclidean case.

Lemma. Let $V$ be an  Euclidean  finite-dimensional
vector space,
and $A$ a symmetric $k$-multilinear form. We have
$
\sup_{\Vert T\Vert=1} \vert{A T^k}\vert
=\sup_{\Vert{T_j}\Vert=1} \vert{AT_1\dots T_k}\vert.
$


This lemma is a consequence of the 1928 paper by O.D. Kellogg
[MR1544896]. This is not true in the non-Euclidean case
where the inequality
$$
\sup_{\Vert T\Vert=1} \vert{A T^k}\vert
\le \kappa_k\sup_{\Vert{T_j}\Vert=1} \vert{AT_1\dots T_k}\vert.
$$
holds true in general with the best constant
$
\kappa_{k}= k^k/k!.
$