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

$$ \begin{aligned} P(x) &= 3x^2-x+10 \\ Q(x) &= 9x^2-2x-1 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & 3x^2 & -x & 10 \\ \color{red}{ - } & 9x^2 & -2x & -1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 3x^2 & -x & 10 \\ \color{red}{ - } & -9x^2 & 2x & 1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & 3x^2 & -x & 10 \\ \color{red}{ - } & -9x^2 & 2x & 1 \\ \hline & 12x^2 & -3x & 9 \end{array} $$

Polynomial Operations Calculator