We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{7x} & \color{blue}{-8} \\ \hline \color{blue}{910x^2} & & & \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{9} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{7x} & \color{blue}{-8} \\ \hline \color{blue}{910x^2} & \color{orangered}{-3640x^4} & \color{orangered}{6370x^3} & \color{orangered}{-7280x^2} \\ \hline \color{blue}{3x} & \color{orangered}{-12x^3} & \color{orangered}{21x^2} & \color{orangered}{-24x} \\ \hline \color{blue}{9} & \color{orangered}{-36x^2} & \color{orangered}{63x} & \color{orangered}{-72} \\ \hline \end{darray} $$

Combine like terms:

$$ -3640x^4 + 6370x^3-12x^3-7280x^2 + 21x^2-36x^2-24x + 63x-72 = \\ -3640x^4+6358x^3-7295x^2+39x-72 $$

Polynomial Operations Calculator