Question
Multiply polynomial $ \, \color{blue}{ m+8 } \, $ by $ \, \color{orangered}{ 2m^3+m^2+3m }$.
Answer
$$ \left( \color{blue}{m+8} \right) \cdot \left( \color{orangered}{2m^3+m^2+3m} \right) = 2m^4+17m^3+11m^2+24m $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2m^3} & \color{blue}{m^2} & \color{blue}{3m} \\ \hline \color{blue}{m} & & & \\ \hline \color{blue}{8} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2m^3} & \color{blue}{m^2} & \color{blue}{3m} \\ \hline \color{blue}{m} & \color{orangered}{2m^4} & \color{orangered}{m^3} & \color{orangered}{3m^2} \\ \hline \color{blue}{8} & \color{orangered}{16m^3} & \color{orangered}{8m^2} & \color{orangered}{24m} \\ \hline \end{darray} $$Combine like terms:
$$ 2m^4 + m^3 + 16m^3 + 3m^2 + 8m^2 + 24m = \\ 2m^4+17m^3+11m^2+24m $$This page was created using
Polynomial Operations Calculator