We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-2x} & \color{blue}{8} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{5x} & & & \\ \hline \color{blue}{-7} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-2x} & \color{blue}{8} \\ \hline \color{blue}{2x^2} & \color{orangered}{2x^4} & \color{orangered}{-4x^3} & \color{orangered}{16x^2} \\ \hline \color{blue}{5x} & \color{orangered}{5x^3} & \color{orangered}{-10x^2} & \color{orangered}{40x} \\ \hline \color{blue}{-7} & \color{orangered}{-7x^2} & \color{orangered}{14x} & \color{orangered}{-56} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^4-4x^3 + 5x^3 + 16x^2-10x^2-7x^2 + 40x + 14x-56 = \\ 2x^4+x^3-x^2+54x-56 $$

Polynomial Operations Calculator