Multiply polynomial $ \, \color{blue}{ 5x-1 } \, $ by $ \, \color{orangered}{ x^2+4x+4 }$.

$$ \left( \color{blue}{5x-1} \right) \cdot \left( \color{orangered}{x^2+4x+4} \right) = 5x^3+19x^2+16x-4 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{4} \\ \hline \color{blue}{5x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{4} \\ \hline \color{blue}{5x} & \color{orangered}{5x^3} & \color{orangered}{20x^2} & \color{orangered}{20x} \\ \hline \color{blue}{-1} & \color{orangered}{-x^2} & \color{orangered}{-4x} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ 5x^3 + 20x^2-x^2 + 20x-4x-4 = \\ 5x^3+19x^2+16x-4 $$

Polynomial Operations Calculator