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

$$ \begin{aligned} P(x) &= 4a^2+2a-4 \\ Q(x) &= -12a^2+2a-14 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 4a^2 & 2a & -4 \\ \color{red}{ - } & -12a^2 & 2a & -14 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 4a^2 & 2a & -4 \\ \color{red}{ - } & 12a^2 & -2a & 14 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 4a^2 & 2a & -4 \\ \color{red}{ - } & 12a^2 & -2a & 14 \\ \hline & -8a^2 & 4a & -18 \end{array} $$

Polynomial Operations Calculator