We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5b^2} & \color{blue}{8b} & \color{blue}{1} \\ \hline \color{blue}{2b^2} & & & \\ \hline \color{blue}{-4b} & & & \\ \hline \color{blue}{-7} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5b^2} & \color{blue}{8b} & \color{blue}{1} \\ \hline \color{blue}{2b^2} & \color{orangered}{10b^4} & \color{orangered}{16b^3} & \color{orangered}{2b^2} \\ \hline \color{blue}{-4b} & \color{orangered}{-20b^3} & \color{orangered}{-32b^2} & \color{orangered}{-4b} \\ \hline \color{blue}{-7} & \color{orangered}{-35b^2} & \color{orangered}{-56b} & \color{orangered}{-7} \\ \hline \end{darray} $$

Combine like terms:

$$ 10b^4 + 16b^3-20b^3 + 2b^2-32b^2-35b^2-4b-56b-7 = \\ 10b^4-4b^3-65b^2-60b-7 $$

Polynomial Operations Calculator