We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3x^2} & \color{blue}{2x} & \color{blue}{-1} \\ \hline \color{blue}{-3x^2} & & & \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{8} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3x^2} & \color{blue}{2x} & \color{blue}{-1} \\ \hline \color{blue}{-3x^2} & \color{orangered}{9x^4} & \color{orangered}{-6x^3} & \color{orangered}{3x^2} \\ \hline \color{blue}{x} & \color{orangered}{-3x^3} & \color{orangered}{2x^2} & \color{orangered}{-x} \\ \hline \color{blue}{8} & \color{orangered}{-24x^2} & \color{orangered}{16x} & \color{orangered}{-8} \\ \hline \end{darray} $$

Combine like terms:

$$ 9x^4-6x^3-3x^3 + 3x^2 + 2x^2-24x^2-x + 16x-8 = \\ 9x^4-9x^3-19x^2+15x-8 $$

Polynomial Operations Calculator