Multiply polynomial $ \, \color{blue}{ r^2+r+1 } \, $ by $ \, \color{orangered}{ 3r-4 }$.

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

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{r^2} & \color{blue}{r} & \color{blue}{1} \\ \hline \color{blue}{3r} & & & \\ \hline \color{blue}{-4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 3r^3 + 3r^2-4r^2 + 3r-4r-4 = \\ 3r^3-r^2-r-4 $$

Polynomial Operations Calculator