Multiply polynomial $ \, \color{blue}{ n^2+n+1 } \, $ by $ \, \color{orangered}{ 2n-2 }$.

$$ \left( \color{blue}{n^2+n+1} \right) \cdot \left( \color{orangered}{2n-2} \right) = 2n^3-2 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{n^2} & \color{blue}{n} & \color{blue}{1} \\ \hline \color{blue}{2n} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{n^2} & \color{blue}{n} & \color{blue}{1} \\ \hline \color{blue}{2n} & \color{orangered}{2n^3} & \color{orangered}{2n^2} & \color{orangered}{2n} \\ \hline \color{blue}{-2} & \color{orangered}{-2n^2} & \color{orangered}{-2n} & \color{orangered}{-2} \\ \hline \end{darray} $$

Combine like terms:

$$ 2n^3 + 2n^2-2n^2 + 2n-2n-2 = \\ 2n^3-2 $$

Polynomial Operations Calculator