We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{50x^3} & \color{blue}{40x^2} & \color{blue}{8x} \\ \hline \color{blue}{9x^2} & & & \\ \hline \color{blue}{-24x} & & & \\ \hline \color{blue}{16} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{50x^3} & \color{blue}{40x^2} & \color{blue}{8x} \\ \hline \color{blue}{9x^2} & \color{orangered}{450x^5} & \color{orangered}{360x^4} & \color{orangered}{72x^3} \\ \hline \color{blue}{-24x} & \color{orangered}{-1200x^4} & \color{orangered}{-960x^3} & \color{orangered}{-192x^2} \\ \hline \color{blue}{16} & \color{orangered}{800x^3} & \color{orangered}{640x^2} & \color{orangered}{128x} \\ \hline \end{darray} $$

Combine like terms:

$$ 450x^5 + 360x^4-1200x^4 + 72x^3-960x^3 + 800x^3-192x^2 + 640x^2 + 128x = \\ 450x^5-840x^4-88x^3+448x^2+128x $$

Polynomial Operations Calculator