Multiply polynomial $ \, \color{blue}{ 2u^2-u-3 } \, $ by $ \, \color{orangered}{ 6u-5 }$.

$$ \left( \color{blue}{2u^2-u-3} \right) \cdot \left( \color{orangered}{6u-5} \right) = 12u^3-16u^2-13u+15 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2u^2} & \color{blue}{-u} & \color{blue}{-3} \\ \hline \color{blue}{6u} & & & \\ \hline \color{blue}{-5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2u^2} & \color{blue}{-u} & \color{blue}{-3} \\ \hline \color{blue}{6u} & \color{orangered}{12u^3} & \color{orangered}{-6u^2} & \color{orangered}{-18u} \\ \hline \color{blue}{-5} & \color{orangered}{-10u^2} & \color{orangered}{5u} & \color{orangered}{15} \\ \hline \end{darray} $$

Combine like terms:

$$ 12u^3-6u^2-10u^2-18u + 5u + 15 = \\ 12u^3-16u^2-13u+15 $$

Polynomial Operations Calculator