We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{8x^2} & \color{blue}{-3x} & \color{blue}{-6} \\ \hline \color{blue}{2x^2} & \color{orangered}{16x^4} & \color{orangered}{-6x^3} & \color{orangered}{-12x^2} \\ \hline \color{blue}{4x} & \color{orangered}{32x^3} & \color{orangered}{-12x^2} & \color{orangered}{-24x} \\ \hline \color{blue}{1} & \color{orangered}{8x^2} & \color{orangered}{-3x} & \color{orangered}{-6} \\ \hline \end{darray} $$

Combine like terms:

$$ 16x^4-6x^3 + 32x^3-12x^2-12x^2 + 8x^2-24x-3x-6 = \\ 16x^4+26x^3-16x^2-27x-6 $$

Polynomial Operations Calculator