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

$$ \left( \color{blue}{-4m^3-2m-1} \right) - \left( \color{orangered}{-5m^3+4m^2+9} \right) = m^3-4m^2-2m-10 $$

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

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

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

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

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

$$ \begin{array}{lrrrr} & -4m^3 & & -2m & -1 \\ \color{red}{ - } & 5m^3 & -4m^2 & & -9 \\ \hline & -9m^3 & 4m^2 & -2m & 8 \end{array} $$

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