We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 2x^4-3x^3-6x^3 + x^2 + 9x^2-2x-3x + 6 = \\ 2x^4-9x^3+10x^2-5x+6 $$

Polynomial Operations Calculator