We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{3x^2} & \color{blue}{-6x} & \color{blue}{-8} \\ \hline \color{blue}{2x} & & & & \\ \hline \color{blue}{5} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{3x^2} & \color{blue}{-6x} & \color{blue}{-8} \\ \hline \color{blue}{2x} & \color{orangered}{2x^4} & \color{orangered}{6x^3} & \color{orangered}{-12x^2} & \color{orangered}{-16x} \\ \hline \color{blue}{5} & \color{orangered}{5x^3} & \color{orangered}{15x^2} & \color{orangered}{-30x} & \color{orangered}{-40} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^4 + 6x^3 + 5x^3-12x^2 + 15x^2-16x-30x-40 = \\ 2x^4+11x^3+3x^2-46x-40 $$

Polynomial Operations Calculator