We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{-4} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{2x^3} & \color{orangered}{-4x^2} \\ \hline \color{blue}{-3x} & \color{orangered}{-3x^3} & \color{orangered}{-6x^2} & \color{orangered}{12x} \\ \hline \color{blue}{1} & \color{orangered}{x^2} & \color{orangered}{2x} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 2x^3-3x^3-4x^2-6x^2 + x^2 + 12x + 2x-4 = \\ x^4-x^3-9x^2+14x-4 $$

Polynomial Operations Calculator