Multiply polynomial $ \, \color{blue}{ -2x-6 } \, $ by $ \, \color{orangered}{ -7x^2+6x+9 }$.

$$ \left( \color{blue}{-2x-6} \right) \cdot \left( \color{orangered}{-7x^2+6x+9} \right) = 14x^3+30x^2-54x-54 $$

We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-7x^2} & \color{blue}{6x} & \color{blue}{9} \\ \hline \color{blue}{-2x} & \color{orangered}{14x^3} & \color{orangered}{-12x^2} & \color{orangered}{-18x} \\ \hline \color{blue}{-6} & \color{orangered}{42x^2} & \color{orangered}{-36x} & \color{orangered}{-54} \\ \hline \end{darray} $$

Combine like terms:

$$ 14x^3-12x^2 + 42x^2-18x-36x-54 = \\ 14x^3+30x^2-54x-54 $$

Polynomial Operations Calculator