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

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

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-2x} & \color{blue}{2} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-2x} & \color{blue}{2} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-2x^3} & \color{orangered}{2x^2} \\ \hline \color{blue}{-1} & \color{orangered}{-x^2} & \color{orangered}{2x} & \color{orangered}{-2} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4-2x^3-x^2 + 2x^2 + 2x-2 = \\ x^4-2x^3+x^2+2x-2 $$

Polynomial Operations Calculator