Multiply polynomial $ \, \color{blue}{ 2v^2+4v+2 } \, $ by $ \, \color{orangered}{ 2v+4 }$.

$$ \left( \color{blue}{2v^2+4v+2} \right) \cdot \left( \color{orangered}{2v+4} \right) = 4v^3+16v^2+20v+8 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2v^2} & \color{blue}{4v} & \color{blue}{2} \\ \hline \color{blue}{2v} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2v^2} & \color{blue}{4v} & \color{blue}{2} \\ \hline \color{blue}{2v} & \color{orangered}{4v^3} & \color{orangered}{8v^2} & \color{orangered}{4v} \\ \hline \color{blue}{4} & \color{orangered}{8v^2} & \color{orangered}{16v} & \color{orangered}{8} \\ \hline \end{darray} $$

Combine like terms:

$$ 4v^3 + 8v^2 + 8v^2 + 4v + 16v + 8 = \\ 4v^3+16v^2+20v+8 $$

Polynomial Operations Calculator