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

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

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ m^4-2m^3-m^3 + m^2 + 2m^2 + 2m^2-m-4m + 2 = \\ m^4-3m^3+5m^2-5m+2 $$

Polynomial Operations Calculator