We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{3x^2} & \color{blue}{3x} & \color{blue}{1} \\ \hline \color{blue}{x} & \color{orangered}{x^4} & \color{orangered}{3x^3} & \color{orangered}{3x^2} & \color{orangered}{x} \\ \hline \color{blue}{-2} & \color{orangered}{-2x^3} & \color{orangered}{-6x^2} & \color{orangered}{-6x} & \color{orangered}{-2} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 3x^3-2x^3 + 3x^2-6x^2 + x-6x-2 = \\ x^4+x^3-3x^2-5x-2 $$

Polynomial Operations Calculator