Add $ \, \color{blue}{ 9p-12-3p^2 } \, $ and $ \, \color{orangered}{ -9+2p^2+4p }$.

$$ \left( \color{blue}{9p-12-3p^2} \right) + \left( \color{orangered}{-9+2p^2+4p} \right) = -p^2+13p-21 $$

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

$$ \begin{aligned} P(x) &= -3p^2+9p-12 \\ Q(x) &= 2p^2+4p-9 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & -3p^2 & 9p & -12 \\ \color{blue}{ + } & 2p^2 & 4p & -9 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & -3p^2 & 9p & -12 \\ \color{blue}{ + } & 2p^2 & 4p & -9 \\ \hline & -p^2 & 13p & -21 \end{array} $$

Polynomial Operations Calculator