Subtract polynomials: $ \, \color{blue}{ 5x^3+5x^2+5 } \, $ , $ \, \color{orangered}{ 6x^3-5x^2+18x-5 }$.

$$ \left( \color{blue}{5x^3+5x^2+5} \right) - \left( \color{orangered}{6x^3-5x^2+18x-5} \right) = -x^3+10x^2-18x+10 $$

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

$$ \begin{array}{lrrrr} & 5x^3 & 5x^2 & & 5 \\ \color{red}{ - } & 6x^3 & -5x^2 & 18x & -5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 5x^3 & 5x^2 & & 5 \\ \color{red}{ - } & -6x^3 & 5x^2 & -18x & 5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 5x^3 & 5x^2 & & 5 \\ \color{red}{ - } & -6x^3 & 5x^2 & -18x & 5 \\ \hline & 11x^3 & & 18x & \end{array} $$

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