We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-x^2} & \color{blue}{-3x} & \color{blue}{4} \\ \hline \color{blue}{3x^2} & \color{orangered}{-3x^4} & \color{orangered}{-9x^3} & \color{orangered}{12x^2} \\ \hline \color{blue}{2x} & \color{orangered}{-2x^3} & \color{orangered}{-6x^2} & \color{orangered}{8x} \\ \hline \color{blue}{-1} & \color{orangered}{x^2} & \color{orangered}{3x} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ -3x^4-9x^3-2x^3 + 12x^2-6x^2 + x^2 + 8x + 3x-4 = \\ -3x^4-11x^3+7x^2+11x-4 $$

Polynomial Operations Calculator