Subtract polynomials: $ \, \color{blue}{ 9q^4+2q^2-4 } \, $ , $ \, \color{orangered}{ q^3+8q^2-5 }$.

$$ \left( \color{blue}{9q^4+2q^2-4} \right) - \left( \color{orangered}{q^3+8q^2-5} \right) = 9q^4-q^3-6q^2+1 $$

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

$$ \begin{array}{lrrrr} & 9q^4 & & 2q^2 & -4 \\ \color{red}{ - } & & q^3 & 8q^2 & -5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 9q^4 & & 2q^2 & -4 \\ \color{red}{ - } & & -q^3 & -8q^2 & 5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 9q^4 & & 2q^2 & -4 \\ \color{red}{ - } & & -q^3 & -8q^2 & 5 \\ \hline & 9q^4 & q^3 & 10q^2 & -9 \end{array} $$

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