Add $ \, \color{blue}{ -n^4+6n^2-2 } \, $ and $ \, \color{orangered}{ 4n^2+7+2n^4 }$.

$$ \left( \color{blue}{-n^4+6n^2-2} \right) + \left( \color{orangered}{4n^2+7+2n^4} \right) = n^4+10n^2+5 $$

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

$$ \begin{aligned} P(x) &= -n^4+6n^2-2 \\ Q(x) &= 2n^4+4n^2+7 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -n^4 & 6n^2 & -2 \\ \color{blue}{ + } & 2n^4 & 4n^2 & 7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -n^4 & 6n^2 & -2 \\ \color{blue}{ + } & 2n^4 & 4n^2 & 7 \\ \hline & n^4 & 10n^2 & 5 \end{array} $$

Polynomial Operations Calculator