Subtract polynomials: $ \, \color{blue}{ 15x^3-3x^2-1 } \, $ , $ \, \color{orangered}{ 10x^3-4x^2+14 }$.

$$ \left( \color{blue}{15x^3-3x^2-1} \right) - \left( \color{orangered}{10x^3-4x^2+14} \right) = 5x^3+x^2-15 $$

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

$$ \begin{array}{lrrr} & 15x^3 & -3x^2 & -1 \\ \color{red}{ - } & 10x^3 & -4x^2 & 14 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 15x^3 & -3x^2 & -1 \\ \color{red}{ - } & -10x^3 & 4x^2 & -14 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 15x^3 & -3x^2 & -1 \\ \color{red}{ - } & -10x^3 & 4x^2 & -14 \\ \hline & 25x^3 & -7x^2 & 13 \end{array} $$

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