We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{300x^3} & \color{blue}{15x} & \color{blue}{-90} \\ \hline \color{blue}{80x} & & & \\ \hline \color{blue}{100} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{300x^3} & \color{blue}{15x} & \color{blue}{-90} \\ \hline \color{blue}{80x} & \color{orangered}{24000x^4} & \color{orangered}{1200x^2} & \color{orangered}{-7200x} \\ \hline \color{blue}{100} & \color{orangered}{30000x^3} & \color{orangered}{1500x} & \color{orangered}{-9000} \\ \hline \end{darray} $$

Combine like terms:

$$ 24000x^4 + 1200x^2 + 30000x^3-7200x + 1500x-9000 = \\ 24000x^4+30000x^3+1200x^2-5700x-9000 $$

Polynomial Operations Calculator