Multiply polynomial $ \, \color{blue}{ 4c+1 } \, $ by $ \, \color{orangered}{ -4c^2+3c-1 }$.

$$ \left( \color{blue}{4c+1} \right) \cdot \left( \color{orangered}{-4c^2+3c-1} \right) = -16c^3+8c^2-c-1 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4c^2} & \color{blue}{3c} & \color{blue}{-1} \\ \hline \color{blue}{4c} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4c^2} & \color{blue}{3c} & \color{blue}{-1} \\ \hline \color{blue}{4c} & \color{orangered}{-16c^3} & \color{orangered}{12c^2} & \color{orangered}{-4c} \\ \hline \color{blue}{1} & \color{orangered}{-4c^2} & \color{orangered}{3c} & \color{orangered}{-1} \\ \hline \end{darray} $$

Combine like terms:

$$ -16c^3 + 12c^2-4c^2-4c + 3c-1 = \\ -16c^3+8c^2-c-1 $$

Polynomial Operations Calculator