Subtract polynomials: $ \, \color{blue}{ 5y^2-6y-11 } \, $ , $ \, \color{orangered}{ 6y^2+2y+5 }$.

$$ \left( \color{blue}{5y^2-6y-11} \right) - \left( \color{orangered}{6y^2+2y+5} \right) = -y^2-8y-16 $$

Step 1: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrrr} & 5y^2 & -6y & -11 \\ \color{red}{ - } & 6y^2 & 2y & 5 \\ \hline \end{array} $$

Step 2: Change ALL the signs in the second row.

$$ \begin{array}{lrrr} & 5y^2 & -6y & -11 \\ \color{red}{ - } & -6y^2 & -2y & -5 \\ \hline \end{array} $$

Step 3: Combine like terms (add each column):

$$ \begin{array}{lrrr} & 5y^2 & -6y & -11 \\ \color{red}{ - } & -6y^2 & -2y & -5 \\ \hline & 11y^2 & -4y & -6 \end{array} $$

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