Multiply polynomial $ \, \color{blue}{ 4n^2-5n+4 } \, $ by $ \, \color{orangered}{ 8n-1 }$.

$$ \left( \color{blue}{4n^2-5n+4} \right) \cdot \left( \color{orangered}{8n-1} \right) = 32n^3-44n^2+37n-4 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4n^2} & \color{blue}{-5n} & \color{blue}{4} \\ \hline \color{blue}{8n} & \color{orangered}{32n^3} & \color{orangered}{-40n^2} & \color{orangered}{32n} \\ \hline \color{blue}{-1} & \color{orangered}{-4n^2} & \color{orangered}{5n} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ 32n^3-40n^2-4n^2 + 32n + 5n-4 = \\ 32n^3-44n^2+37n-4 $$

Polynomial Operations Calculator