Subtract polynomials: $ \, \color{blue}{ 6q^4-q^3+9q^2+6q+4 } \, $ , $ \, \color{orangered}{ 6q^4+7q^3+2q^2-3q }$.

$$ \left( \color{blue}{6q^4-q^3+9q^2+6q+4} \right) - \left( \color{orangered}{6q^4+7q^3+2q^2-3q} \right) = -8q^3+7q^2+9q+4 $$

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

$$ \begin{array}{lrrrrr} & 6q^4 & -q^3 & 9q^2 & 6q & 4 \\ \color{red}{ - } & 6q^4 & 7q^3 & 2q^2 & -3q & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 6q^4 & -q^3 & 9q^2 & 6q & 4 \\ \color{red}{ - } & -6q^4 & -7q^3 & -2q^2 & 3q & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 6q^4 & -q^3 & 9q^2 & 6q & 4 \\ \color{red}{ - } & -6q^4 & -7q^3 & -2q^2 & 3q & \\ \hline & 12q^4 & 6q^3 & 11q^2 & 3q & 4 \end{array} $$

Polynomial Operations Calculator