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

$$ \left( \color{blue}{a+4} \right) \cdot \left( \color{orangered}{4a^2-a+4} \right) = 4a^3+15a^2+16 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 4a^3-a^2 + 16a^2 + 4a-4a + 16 = \\ 4a^3+15a^2+16 $$

Polynomial Operations Calculator