Multiply polynomial $ \, \color{blue}{ x^2-3x-54 } \, $ by $ \, \color{orangered}{ x+6 }$.

$$ \left( \color{blue}{x^2-3x-54} \right) \cdot \left( \color{orangered}{x+6} \right) = x^3+3x^2-72x-324 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-3x} & \color{blue}{-54} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{6} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-3x} & \color{blue}{-54} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-3x^2} & \color{orangered}{-54x} \\ \hline \color{blue}{6} & \color{orangered}{6x^2} & \color{orangered}{-18x} & \color{orangered}{-324} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3-3x^2 + 6x^2-54x-18x-324 = \\ x^3+3x^2-72x-324 $$

Polynomial Operations Calculator