The primary application of expand is to distribute products over sums. This is done for all polynomials. For quotients of polynomials, only sums in the numerator are expanded; products and powers are left alone.

The expand(M) function computes the element-wise expansion of M.  The result, R, is formed as R[i,j] = expand(M[i,j]).

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$M≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=a\left(x+y\right)\right)\:$

$\mathrm{expand}\left(M\right)$

$\left[\begin{array}{ccc}ax+ay& ax+ay& ax+ay\\ ax+ay& ax+ay& ax+ay\end{array}\right]$