Question
Multiply polynomial $ \, \color{blue}{ 2n^2-8n-4 } \, $ by $ \, \color{orangered}{ 3n+2 }$.
Answer
$$ \left( \color{blue}{2n^2-8n-4} \right) \cdot \left( \color{orangered}{3n+2} \right) = 6n^3-20n^2-28n-8 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2n^2} & \color{blue}{-8n} & \color{blue}{-4} \\ \hline \color{blue}{3n} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2n^2} & \color{blue}{-8n} & \color{blue}{-4} \\ \hline \color{blue}{3n} & \color{orangered}{6n^3} & \color{orangered}{-24n^2} & \color{orangered}{-12n} \\ \hline \color{blue}{2} & \color{orangered}{4n^2} & \color{orangered}{-16n} & \color{orangered}{-8} \\ \hline \end{darray} $$Combine like terms:
$$ 6n^3-24n^2 + 4n^2-12n-16n-8 = \\ 6n^3-20n^2-28n-8 $$This page was created using
Polynomial Operations Calculator