Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lr} & 4444 \\ \color{blue}{ + } & 5555 \\ \hline \end{array} $$Step 2: Combine like terms (add each column):
$$ \begin{array}{lr} & 4444 \\ \color{blue}{ + } & 5555 \\ \hline & 9999 \end{array} $$