Subtract polynomials: $ \, \color{blue}{ 7x^9+9x^5+15 } \, $ , $ \, \color{orangered}{ 10x^9+8x^5+12 }$.

$$ \left( \color{blue}{7x^9+9x^5+15} \right) - \left( \color{orangered}{10x^9+8x^5+12} \right) = -3x^9+x^5+3 $$

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

$$ \begin{array}{lrrr} & 7x^9 & 9x^5 & 15 \\ \color{red}{ - } & 10x^9 & 8x^5 & 12 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 7x^9 & 9x^5 & 15 \\ \color{red}{ - } & -10x^9 & -8x^5 & -12 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 7x^9 & 9x^5 & 15 \\ \color{red}{ - } & -10x^9 & -8x^5 & -12 \\ \hline & 17x^9 & 17x^5 & 27 \end{array} $$

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