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

$$ \left( \color{blue}{3v^4-2+8v^2} \right) + \left( \color{orangered}{6v^2+4-7v^4} \right) = -4v^4+14v^2+2 $$

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

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

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

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

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

$$ \begin{array}{lrrr} & 3v^4 & 8v^2 & -2 \\ \color{blue}{ + } & -7v^4 & 6v^2 & 4 \\ \hline & -4v^4 & 14v^2 & 2 \end{array} $$

Polynomial Operations Calculator