We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{b^2} & \color{blue}{-3b} & \color{blue}{-6} \\ \hline \color{blue}{b^2} & \color{orangered}{b^4} & \color{orangered}{-3b^3} & \color{orangered}{-6b^2} \\ \hline \color{blue}{-8b} & \color{orangered}{-8b^3} & \color{orangered}{24b^2} & \color{orangered}{48b} \\ \hline \color{blue}{-3} & \color{orangered}{-3b^2} & \color{orangered}{9b} & \color{orangered}{18} \\ \hline \end{darray} $$

Combine like terms:

$$ b^4-3b^3-8b^3-6b^2 + 24b^2-3b^2 + 48b + 9b + 18 = \\ b^4-11b^3+15b^2+57b+18 $$

Polynomial Operations Calculator