Subtract polynomials: $ \, \color{blue}{ 4g^3+6g^2+3g+9 } \, $ , $ \, \color{orangered}{ 3g^3+5g^2+g+1 }$.

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

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

$$ \begin{array}{lrrrr} & 4g^3 & 6g^2 & 3g & 9 \\ \color{red}{ - } & 3g^3 & 5g^2 & g & 1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 4g^3 & 6g^2 & 3g & 9 \\ \color{red}{ - } & -3g^3 & -5g^2 & -g & -1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 4g^3 & 6g^2 & 3g & 9 \\ \color{red}{ - } & -3g^3 & -5g^2 & -g & -1 \\ \hline & 7g^3 & 11g^2 & 4g & 10 \end{array} $$

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