Subtract polynomials: $ \, \color{blue}{ 8x^3-10x^2+30 } \, $ , $ \, \color{orangered}{ 4x^3-7x^2-6 }$.

$$ \left( \color{blue}{8x^3-10x^2+30} \right) - \left( \color{orangered}{4x^3-7x^2-6} \right) = 4x^3-3x^2+36 $$

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

$$ \begin{array}{lrrr} & 8x^3 & -10x^2 & 30 \\ \color{red}{ - } & 4x^3 & -7x^2 & -6 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 8x^3 & -10x^2 & 30 \\ \color{red}{ - } & -4x^3 & 7x^2 & 6 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 8x^3 & -10x^2 & 30 \\ \color{red}{ - } & -4x^3 & 7x^2 & 6 \\ \hline & 12x^3 & -17x^2 & 24 \end{array} $$

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