We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{3} \\ \hline \color{blue}{4x} & \color{orangered}{4x^3} & \color{orangered}{8x^2} & \color{orangered}{12x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^2} & \color{orangered}{-8x} & \color{orangered}{-12} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^3 + 8x^2-4x^2 + 12x-8x-12 = \\ 4x^3+4x^2+4x-12 $$

Polynomial Operations Calculator