We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-x} & \color{blue}{-3} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-x^3} & \color{orangered}{-3x^2} \\ \hline \color{blue}{4x} & \color{orangered}{4x^3} & \color{orangered}{-4x^2} & \color{orangered}{-12x} \\ \hline \color{blue}{2} & \color{orangered}{2x^2} & \color{orangered}{-2x} & \color{orangered}{-6} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4-x^3 + 4x^3-3x^2-4x^2 + 2x^2-12x-2x-6 = \\ x^4+3x^3-5x^2-14x-6 $$

Polynomial Operations Calculator