Add $ \, \color{blue}{ m^3+8m^4+6m } \, $ and $ \, \color{orangered}{ 7m^3+6m-2m^4 }$.

$$ \left( \color{blue}{m^3+8m^4+6m} \right) + \left( \color{orangered}{7m^3+6m-2m^4} \right) = 6m^4+8m^3+12m $$

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

$$ \begin{aligned} P(x) &= 8m^4+m^3+6m \\ Q(x) &= -2m^4+7m^3+6m \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 8m^4 & m^3 & 6m \\ \color{blue}{ + } & -2m^4 & 7m^3 & 6m \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 8m^4 & m^3 & 6m \\ \color{blue}{ + } & -2m^4 & 7m^3 & 6m \\ \hline & 6m^4 & 8m^3 & 12m \end{array} $$

Polynomial Operations Calculator