We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 2x^4-4x^3 + 4x^3-2x^2-8x^2-6x^2-4x + 12x + 6 = \\ 2x^4-16x^2+8x+6 $$

Polynomial Operations Calculator