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

$$ \left( \color{blue}{2x-1} \right) \cdot \left( \color{orangered}{3x^2-3x-1} \right) = 6x^3-9x^2+x+1 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 6x^3-6x^2-3x^2-2x + 3x + 1 = \\ 6x^3-9x^2+x+1 $$

Polynomial Operations Calculator