Multiply polynomial $ \, \color{blue}{ 2n+6 } \, $ by $ \, \color{orangered}{ -6n^2-5n+5 }$.

$$ \left( \color{blue}{2n+6} \right) \cdot \left( \color{orangered}{-6n^2-5n+5} \right) = -12n^3-46n^2-20n+30 $$

We can multiply polynomials by using a GRID METHOD

Write one of the polynomials across the top and the other down the left side.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-6n^2} & \color{blue}{-5n} & \color{blue}{5} \\ \hline \color{blue}{2n} & & & \\ \hline \color{blue}{6} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-6n^2} & \color{blue}{-5n} & \color{blue}{5} \\ \hline \color{blue}{2n} & \color{orangered}{-12n^3} & \color{orangered}{-10n^2} & \color{orangered}{10n} \\ \hline \color{blue}{6} & \color{orangered}{-36n^2} & \color{orangered}{-30n} & \color{orangered}{30} \\ \hline \end{darray} $$

Combine like terms:

$$ -12n^3-10n^2-36n^2 + 10n-30n + 30 = \\ -12n^3-46n^2-20n+30 $$

Polynomial Operations Calculator