We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 3x^4 + 2x^3 + 3x^3-8x^2 + 2x^2 + 6x^2-8x + 4x-16 = \\ 3x^4+5x^3-4x-16 $$

Polynomial Operations Calculator