Add $ \, \color{blue}{ -3-7n^3-4n^2 } \, $ and $ \, \color{orangered}{ 5-3n^3+5n^2 }$.

$$ \left( \color{blue}{-3-7n^3-4n^2} \right) + \left( \color{orangered}{5-3n^3+5n^2} \right) = -10n^3+n^2+2 $$

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

$$ \begin{aligned} P(x) &= -7n^3-4n^2-3 \\ Q(x) &= -3n^3+5n^2+5 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -7n^3 & -4n^2 & -3 \\ \color{blue}{ + } & -3n^3 & 5n^2 & 5 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -7n^3 & -4n^2 & -3 \\ \color{blue}{ + } & -3n^3 & 5n^2 & 5 \\ \hline & -10n^3 & n^2 & 2 \end{array} $$

Polynomial Operations Calculator