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

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

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ r^3-2r^2-r^2 + 3r + 2r-3 = \\ r^3-3r^2+5r-3 $$

Polynomial Operations Calculator