Multiply polynomial $ \, \color{blue}{ 2r+1 } \, $ by $ \, \color{orangered}{ -4r^2+3r-6 }$.

$$ \left( \color{blue}{2r+1} \right) \cdot \left( \color{orangered}{-4r^2+3r-6} \right) = -8r^3+2r^2-9r-6 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4r^2} & \color{blue}{3r} & \color{blue}{-6} \\ \hline \color{blue}{2r} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4r^2} & \color{blue}{3r} & \color{blue}{-6} \\ \hline \color{blue}{2r} & \color{orangered}{-8r^3} & \color{orangered}{6r^2} & \color{orangered}{-12r} \\ \hline \color{blue}{1} & \color{orangered}{-4r^2} & \color{orangered}{3r} & \color{orangered}{-6} \\ \hline \end{darray} $$

Combine like terms:

$$ -8r^3 + 6r^2-4r^2-12r + 3r-6 = \\ -8r^3+2r^2-9r-6 $$

Polynomial Operations Calculator