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

$$ \begin{aligned} P(x) &= x^2-4x+8 \\ Q(x) &= x^2-7x+8 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & x^2 & -4x & 8 \\ \color{red}{ - } & x^2 & -7x & 8 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & x^2 & -4x & 8 \\ \color{red}{ - } & -x^2 & 7x & -8 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & x^2 & -4x & 8 \\ \color{red}{ - } & -x^2 & 7x & -8 \\ \hline & 2x^2 & -11x & 16 \end{array} $$

Polynomial Operations Calculator