We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 9x^3 + 6x^2-6x^2-3x-4x + 2 = \\ 9x^3-7x+2 $$

Polynomial Operations Calculator