Question
Multiply polynomial $ \, \color{blue}{ -9m^6+12m^5 } \, $ by $ \, \color{orangered}{ m^2+2m+1 }$.
Answer
$$ \left( \color{blue}{-9m^6+12m^5} \right) \cdot \left( \color{orangered}{m^2+2m+1} \right) = -9m^8-6m^7+15m^6+12m^5 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{m^2} & \color{blue}{2m} & \color{blue}{1} \\ \hline \color{blue}{-9m^6} & & & \\ \hline \color{blue}{12m^5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{m^2} & \color{blue}{2m} & \color{blue}{1} \\ \hline \color{blue}{-9m^6} & \color{orangered}{-9m^8} & \color{orangered}{-18m^7} & \color{orangered}{-9m^6} \\ \hline \color{blue}{12m^5} & \color{orangered}{12m^7} & \color{orangered}{24m^6} & \color{orangered}{12m^5} \\ \hline \end{darray} $$Combine like terms:
$$ -9m^8-18m^7 + 12m^7-9m^6 + 24m^6 + 12m^5 = \\ -9m^8-6m^7+15m^6+12m^5 $$This page was created using
Polynomial Operations Calculator