Add $ \, \color{blue}{ 1+7r^4-8r } \, $ and $ \, \color{orangered}{ 4r-2r^4-1 }$.

$$ \left( \color{blue}{1+7r^4-8r} \right) + \left( \color{orangered}{4r-2r^4-1} \right) = 5r^4-4r $$

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

$$ \begin{aligned} P(x) &= 7r^4-8r+1 \\ Q(x) &= -2r^4+4r-1 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 7r^4 & -8r & 1 \\ \color{blue}{ + } & -2r^4 & 4r & -1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 7r^4 & -8r & 1 \\ \color{blue}{ + } & -2r^4 & 4r & -1 \\ \hline & 5r^4 & -4r & \end{array} $$

Polynomial Operations Calculator