Subtract polynomials: $ \, \color{blue}{ -2g^3+4g^2-g-8 } \, $ , $ \, \color{orangered}{ -7g^3+g }$.

$$ \left( \color{blue}{-2g^3+4g^2-g-8} \right) - \left( \color{orangered}{-7g^3+g} \right) = 5g^3+4g^2-2g-8 $$

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

$$ \begin{array}{lrrrr} & -2g^3 & 4g^2 & -g & -8 \\ \color{red}{ - } & -7g^3 & & g & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & -2g^3 & 4g^2 & -g & -8 \\ \color{red}{ - } & 7g^3 & & -g & \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & -2g^3 & 4g^2 & -g & -8 \\ \color{red}{ - } & 7g^3 & & -g & \\ \hline & -9g^3 & 4g^2 & & -8 \end{array} $$

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