Question
Multiply polynomial $ \, \color{blue}{ 2m+1 } \, $ by $ \, \color{orangered}{ -2m^2-m-2 }$.
Answer
$$ \left( \color{blue}{2m+1} \right) \cdot \left( \color{orangered}{-2m^2-m-2} \right) = -4m^3-4m^2-5m-2 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-2m^2} & \color{blue}{-m} & \color{blue}{-2} \\ \hline \color{blue}{2m} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-2m^2} & \color{blue}{-m} & \color{blue}{-2} \\ \hline \color{blue}{2m} & \color{orangered}{-4m^3} & \color{orangered}{-2m^2} & \color{orangered}{-4m} \\ \hline \color{blue}{1} & \color{orangered}{-2m^2} & \color{orangered}{-m} & \color{orangered}{-2} \\ \hline \end{darray} $$Combine like terms:
$$ -4m^3-2m^2-2m^2-4m-m-2 = \\ -4m^3-4m^2-5m-2 $$This page was created using
Polynomial Operations Calculator