We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{-2} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-6x} & & & \\ \hline \color{blue}{8} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{x} & \color{blue}{-2} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{x^3} & \color{orangered}{-2x^2} \\ \hline \color{blue}{-6x} & \color{orangered}{-6x^3} & \color{orangered}{-6x^2} & \color{orangered}{12x} \\ \hline \color{blue}{8} & \color{orangered}{8x^2} & \color{orangered}{8x} & \color{orangered}{-16} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + x^3-6x^3-2x^2-6x^2 + 8x^2 + 12x + 8x-16 = \\ x^4-5x^3+20x-16 $$

Polynomial Operations Calculator