Subtract polynomials: $ \, \color{blue}{ s^6+7s^5+2s^4+9s^3+10s^2+12s+15 } \, $ , $ \, \color{orangered}{ s^6+9s^5+8s^4+9s^3+12s^2+15s+20 }$.

$$ \left( \color{blue}{s^6+7s^5+2s^4+9s^3+10s^2+12s+15} \right) - \left( \color{orangered}{s^6+9s^5+8s^4+9s^3+12s^2+15s+20} \right) = -2s^5-6s^4-2s^2-3s-5 $$

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

$$ \begin{array}{lrrrrrrr} & s^6 & 7s^5 & 2s^4 & 9s^3 & 10s^2 & 12s & 15 \\ \color{red}{ - } & s^6 & 9s^5 & 8s^4 & 9s^3 & 12s^2 & 15s & 20 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrrrr} & s^6 & 7s^5 & 2s^4 & 9s^3 & 10s^2 & 12s & 15 \\ \color{red}{ - } & -s^6 & -9s^5 & -8s^4 & -9s^3 & -12s^2 & -15s & -20 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrrrr} & s^6 & 7s^5 & 2s^4 & 9s^3 & 10s^2 & 12s & 15 \\ \color{red}{ - } & -s^6 & -9s^5 & -8s^4 & -9s^3 & -12s^2 & -15s & -20 \\ \hline & 2s^6 & 16s^5 & 10s^4 & 18s^3 & 22s^2 & 27s & 35 \end{array} $$

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