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

$$ \begin{aligned} P(x) &= x^2-1 \\ Q(x) &= -4x+1 \\ \end{aligned} $$

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

$$ \begin{array}{lrrr} & x^2 & & -1 \\ \color{red}{ - } & & -4x & 1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & x^2 & & -1 \\ \color{red}{ - } & & 4x & -1 \\ \hline \end{array} $$

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

$$ \begin{array}{lrrr} & x^2 & & -1 \\ \color{red}{ - } & & 4x & -1 \\ \hline & x^2 & -4x & \end{array} $$

Polynomial Operations Calculator