Multiply polynomial $ \, \color{blue}{ 2b^2+5 } \, $ by $ \, \color{orangered}{ 2b^3-2b-3 }$.

$$ \left( \color{blue}{2b^2+5} \right) \cdot \left( \color{orangered}{2b^3-2b-3} \right) = 4b^5+6b^3-6b^2-10b-15 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 4b^5-4b^3 + 10b^3-6b^2-10b-15 = \\ 4b^5+6b^3-6b^2-10b-15 $$

Polynomial Operations Calculator