Subtract polynomials: $ \, \color{blue}{ 3q^4+3q^3+7q^2+q+9 } \, $ , $ \, \color{orangered}{ 3q^4+q^3+5q^2+q+7 }$.

$$ \left( \color{blue}{3q^4+3q^3+7q^2+q+9} \right) - \left( \color{orangered}{3q^4+q^3+5q^2+q+7} \right) = 2q^3+2q^2+2 $$

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

$$ \begin{array}{lrrrrr} & 3q^4 & 3q^3 & 7q^2 & q & 9 \\ \color{red}{ - } & 3q^4 & q^3 & 5q^2 & q & 7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 3q^4 & 3q^3 & 7q^2 & q & 9 \\ \color{red}{ - } & -3q^4 & -q^3 & -5q^2 & -q & -7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & 3q^4 & 3q^3 & 7q^2 & q & 9 \\ \color{red}{ - } & -3q^4 & -q^3 & -5q^2 & -q & -7 \\ \hline & 6q^4 & 4q^3 & 12q^2 & 2q & 16 \end{array} $$

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