Subtract polynomials: $ \, \color{blue}{ 4n-3n^3 } \, $ , $ \, \color{orangered}{ 3n^3+4n }$.

$$ \left( \color{blue}{4n-3n^3} \right) - \left( \color{orangered}{3n^3+4n} \right) = -6n^3 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -3n^3+4n \\ Q(x) &= 3n^3+4n \\ \end{aligned} $$

Step 2: Write second polynomial below the first one. Making sure like terms are lined up.

$$ \begin{array}{lrr} & -3n^3 & 4n \\ \color{red}{ - } & 3n^3 & 4n \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrr} & -3n^3 & 4n \\ \color{red}{ - } & -3n^3 & -4n \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrr} & -3n^3 & 4n \\ \color{red}{ - } & -3n^3 & -4n \\ \hline & & 8n \end{array} $$

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