We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{-4x^2} & \color{blue}{x} & \color{blue}{6} \\ \hline \color{blue}{x} & & & & \\ \hline \color{blue}{1} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{-4x^2} & \color{blue}{x} & \color{blue}{6} \\ \hline \color{blue}{x} & \color{orangered}{x^4} & \color{orangered}{-4x^3} & \color{orangered}{x^2} & \color{orangered}{6x} \\ \hline \color{blue}{1} & \color{orangered}{x^3} & \color{orangered}{-4x^2} & \color{orangered}{x} & \color{orangered}{6} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4-4x^3 + x^3 + x^2-4x^2 + 6x + x + 6 = \\ x^4-3x^3-3x^2+7x+6 $$

Polynomial Operations Calculator