Step 1: Write second polynomial below the first one. Making sure like terms are lined up.
$$ \begin{array}{lrrr} & y^2 & 2y & \\ \color{red}{ - } & y^2 & 5y & 8 \\ \hline \end{array} $$Step 2: Change ALL the signs in the second row.
$$ \begin{array}{lrrr} & y^2 & 2y & \\ \color{red}{ - } & -y^2 & -5y & -8 \\ \hline \end{array} $$Step 3: Combine like terms (add each column):
$$ \begin{array}{lrrr} & y^2 & 2y & \\ \color{red}{ - } & -y^2 & -5y & -8 \\ \hline & 2y^2 & 7y & 8 \end{array} $$