Subtract polynomials: $ \, \color{blue}{ -v^3+4v^2-5 } \, $ , $ \, \color{orangered}{ -6v^3-3v^2+3 }$.

$$ \left( \color{blue}{-v^3+4v^2-5} \right) - \left( \color{orangered}{-6v^3-3v^2+3} \right) = 5v^3+7v^2-8 $$

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

$$ \begin{array}{lrrr} & -v^3 & 4v^2 & -5 \\ \color{red}{ - } & -6v^3 & -3v^2 & 3 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -v^3 & 4v^2 & -5 \\ \color{red}{ - } & 6v^3 & 3v^2 & -3 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -v^3 & 4v^2 & -5 \\ \color{red}{ - } & 6v^3 & 3v^2 & -3 \\ \hline & -7v^3 & v^2 & -2 \end{array} $$

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