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

$$ \begin{aligned} P(x) &= k^2+8k-6 \\ Q(x) &= -2k^2-10k+7 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & k^2 & 8k & -6 \\ \color{red}{ - } & -2k^2 & -10k & 7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & k^2 & 8k & -6 \\ \color{red}{ - } & 2k^2 & 10k & -7 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & k^2 & 8k & -6 \\ \color{red}{ - } & 2k^2 & 10k & -7 \\ \hline & -k^2 & -2k & 1 \end{array} $$

Polynomial Operations Calculator