Question
Multiply polynomial $ \, \color{blue}{ m-3 } \, $ by $ \, \color{orangered}{ m^2+3m-4 }$.
Answer
$$ \left( \color{blue}{m-3} \right) \cdot \left( \color{orangered}{m^2+3m-4} \right) = m^3-13m+12 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{m^2} & \color{blue}{3m} & \color{blue}{-4} \\ \hline \color{blue}{m} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{m^2} & \color{blue}{3m} & \color{blue}{-4} \\ \hline \color{blue}{m} & \color{orangered}{m^3} & \color{orangered}{3m^2} & \color{orangered}{-4m} \\ \hline \color{blue}{-3} & \color{orangered}{-3m^2} & \color{orangered}{-9m} & \color{orangered}{12} \\ \hline \end{darray} $$Combine like terms:
$$ m^3 + 3m^2-3m^2-4m-9m + 12 = \\ m^3-13m+12 $$This page was created using
Polynomial Operations Calculator