Subtract polynomials: $ \, \color{blue}{ 2z^{13}+11z^{10}+7z^7+9z^5 } \, $ , $ \, \color{orangered}{ 7z^{14}-7z^{10}+7z^7+4z^5 }$.

$$ \left( \color{blue}{2z^{13}+11z^{10}+7z^7+9z^5} \right) - \left( \color{orangered}{7z^{14}-7z^{10}+7z^7+4z^5} \right) = -7z^{14}+2z^{13}+18z^{10}+5z^5 $$

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

$$ \begin{array}{lrrrrr} & & 2z^{13} & 11z^{10} & 7z^7 & 9z^5 \\ \color{red}{ - } & 7z^{14} & & -7z^{10} & 7z^7 & 4z^5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & & 2z^{13} & 11z^{10} & 7z^7 & 9z^5 \\ \color{red}{ - } & -7z^{14} & & 7z^{10} & -7z^7 & -4z^5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrrr} & & 2z^{13} & 11z^{10} & 7z^7 & 9z^5 \\ \color{red}{ - } & -7z^{14} & & 7z^{10} & -7z^7 & -4z^5 \\ \hline & 7z^{14} & 2z^{13} & 4z^{10} & 14z^7 & 13z^5 \end{array} $$

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