Subtract polynomials: $ \, \color{blue}{ 2x^3+7x+10 } \, $ , $ \, \color{orangered}{ 5x^3+12x^2+10x+8 }$.

$$ \left( \color{blue}{2x^3+7x+10} \right) - \left( \color{orangered}{5x^3+12x^2+10x+8} \right) = -3x^3-12x^2-3x+2 $$

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

$$ \begin{array}{lrrrr} & 2x^3 & & 7x & 10 \\ \color{red}{ - } & 5x^3 & 12x^2 & 10x & 8 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 2x^3 & & 7x & 10 \\ \color{red}{ - } & -5x^3 & -12x^2 & -10x & -8 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrrr} & 2x^3 & & 7x & 10 \\ \color{red}{ - } & -5x^3 & -12x^2 & -10x & -8 \\ \hline & 7x^3 & 12x^2 & 17x & 18 \end{array} $$

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