We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{-8x^2} & \color{blue}{-73x} & \color{blue}{164} \\ \hline \color{blue}{2x} & & & & \\ \hline \color{blue}{-1} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{-8x^2} & \color{blue}{-73x} & \color{blue}{164} \\ \hline \color{blue}{2x} & \color{orangered}{8x^4} & \color{orangered}{-16x^3} & \color{orangered}{-146x^2} & \color{orangered}{328x} \\ \hline \color{blue}{-1} & \color{orangered}{-4x^3} & \color{orangered}{8x^2} & \color{orangered}{73x} & \color{orangered}{-164} \\ \hline \end{darray} $$

Combine like terms:

$$ 8x^4-16x^3-4x^3-146x^2 + 8x^2 + 328x + 73x-164 = \\ 8x^4-20x^3-138x^2+401x-164 $$

Polynomial Operations Calculator