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

$$ \begin{aligned} P(x) &= -8v^3+2v^2+6v \\ Q(x) &= 4v^3-6v^2+5v \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -8v^3 & 2v^2 & 6v \\ \color{red}{ - } & 4v^3 & -6v^2 & 5v \\ \hline \end{array} $$

Step 3: Change ALL the signs in the second row.

$$ \begin{array}{lrrr} & -8v^3 & 2v^2 & 6v \\ \color{red}{ - } & -4v^3 & 6v^2 & -5v \\ \hline \end{array} $$

Step 4: Combine like terms (add each column):

$$ \begin{array}{lrrr} & -8v^3 & 2v^2 & 6v \\ \color{red}{ - } & -4v^3 & 6v^2 & -5v \\ \hline & -4v^3 & -4v^2 & 11v \end{array} $$

Polynomial Operations Calculator