We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^6} & \color{blue}{-10x^4} & \color{blue}{-48x^2} \\ \hline \color{blue}{2x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^6} & \color{blue}{-10x^4} & \color{blue}{-48x^2} \\ \hline \color{blue}{2x} & \color{orangered}{4x^7} & \color{orangered}{-20x^5} & \color{orangered}{-96x^3} \\ \hline \color{blue}{5} & \color{orangered}{10x^6} & \color{orangered}{-50x^4} & \color{orangered}{-240x^2} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^7-20x^5 + 10x^6-96x^3-50x^4-240x^2 = \\ 4x^7+10x^6-20x^5-50x^4-96x^3-240x^2 $$

Polynomial Operations Calculator