Multiply polynomial $ \, \color{blue}{ 6x+9 } \, $ by $ \, \color{orangered}{ 6x^2+4x+5 }$.

$$ \left( \color{blue}{6x+9} \right) \cdot \left( \color{orangered}{6x^2+4x+5} \right) = 36x^3+78x^2+66x+45 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{4x} & \color{blue}{5} \\ \hline \color{blue}{6x} & & & \\ \hline \color{blue}{9} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{4x} & \color{blue}{5} \\ \hline \color{blue}{6x} & \color{orangered}{36x^3} & \color{orangered}{24x^2} & \color{orangered}{30x} \\ \hline \color{blue}{9} & \color{orangered}{54x^2} & \color{orangered}{36x} & \color{orangered}{45} \\ \hline \end{darray} $$

Combine like terms:

$$ 36x^3 + 24x^2 + 54x^2 + 30x + 36x + 45 = \\ 36x^3+78x^2+66x+45 $$

Polynomial Operations Calculator