Question
Multiply polynomial $ \, \color{blue}{ 3v+1 } \, $ by $ \, \color{orangered}{ -3v^2+2v-2 }$.
Answer
$$ \left( \color{blue}{3v+1} \right) \cdot \left( \color{orangered}{-3v^2+2v-2} \right) = -9v^3+3v^2-4v-2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3v^2} & \color{blue}{2v} & \color{blue}{-2} \\ \hline \color{blue}{3v} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3v^2} & \color{blue}{2v} & \color{blue}{-2} \\ \hline \color{blue}{3v} & \color{orangered}{-9v^3} & \color{orangered}{6v^2} & \color{orangered}{-6v} \\ \hline \color{blue}{1} & \color{orangered}{-3v^2} & \color{orangered}{2v} & \color{orangered}{-2} \\ \hline \end{darray} $$Combine like terms:
$$ -9v^3 + 6v^2-3v^2-6v + 2v-2 = \\ -9v^3+3v^2-4v-2 $$This page was created using
Polynomial Operations Calculator