Multiply polynomial $ \, \color{blue}{ x-4 } \, $ by $ \, \color{orangered}{ x^2+4x+16 }$.

$$ \left( \color{blue}{x-4} \right) \cdot \left( \color{orangered}{x^2+4x+16} \right) = x^3-64 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{16} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{4x^2} & \color{orangered}{16x} \\ \hline \color{blue}{-4} & \color{orangered}{-4x^2} & \color{orangered}{-16x} & \color{orangered}{-64} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3 + 4x^2-4x^2 + 16x-16x-64 = \\ x^3-64 $$

Polynomial Operations Calculator