Multiply polynomial $ \, \color{blue}{ -3x-1 } \, $ by $ \, \color{orangered}{ 2x^2+8x+1 }$.

$$ \left( \color{blue}{-3x-1} \right) \cdot \left( \color{orangered}{2x^2+8x+1} \right) = -6x^3-26x^2-11x-1 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{8x} & \color{blue}{1} \\ \hline \color{blue}{-3x} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{8x} & \color{blue}{1} \\ \hline \color{blue}{-3x} & \color{orangered}{-6x^3} & \color{orangered}{-24x^2} & \color{orangered}{-3x} \\ \hline \color{blue}{-1} & \color{orangered}{-2x^2} & \color{orangered}{-8x} & \color{orangered}{-1} \\ \hline \end{darray} $$

Combine like terms:

$$ -6x^3-24x^2-2x^2-3x-8x-1 = \\ -6x^3-26x^2-11x-1 $$

Polynomial Operations Calculator