Multiply polynomial $ \, \color{blue}{ 3x+2 } \, $ by $ \, \color{orangered}{ 3x^2-3x-7 }$.

$$ \left( \color{blue}{3x+2} \right) \cdot \left( \color{orangered}{3x^2-3x-7} \right) = 9x^3-3x^2-27x-14 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{-7} \\ \hline \color{blue}{3x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-3x} & \color{blue}{-7} \\ \hline \color{blue}{3x} & \color{orangered}{9x^3} & \color{orangered}{-9x^2} & \color{orangered}{-21x} \\ \hline \color{blue}{2} & \color{orangered}{6x^2} & \color{orangered}{-6x} & \color{orangered}{-14} \\ \hline \end{darray} $$

Combine like terms:

$$ 9x^3-9x^2 + 6x^2-21x-6x-14 = \\ 9x^3-3x^2-27x-14 $$

Polynomial Operations Calculator