We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-5x} & \color{blue}{-2} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-3x} & & & \\ \hline \color{blue}{6} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-5x} & \color{blue}{-2} \\ \hline \color{blue}{2x^2} & \color{orangered}{4x^4} & \color{orangered}{-10x^3} & \color{orangered}{-4x^2} \\ \hline \color{blue}{-3x} & \color{orangered}{-6x^3} & \color{orangered}{15x^2} & \color{orangered}{6x} \\ \hline \color{blue}{6} & \color{orangered}{12x^2} & \color{orangered}{-30x} & \color{orangered}{-12} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^4-10x^3-6x^3-4x^2 + 15x^2 + 12x^2 + 6x-30x-12 = \\ 4x^4-16x^3+23x^2-24x-12 $$

Polynomial Operations Calculator