Multiply polynomial $ \, \color{blue}{ 3x^2-18x-9 } \, $ by $ \, \color{orangered}{ 2x^2-16x+2 }$.

$$ \left( \color{blue}{3x^2-18x-9} \right) \cdot \left( \color{orangered}{2x^2-16x+2} \right) = 6x^4-84x^3+276x^2+108x-18 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-18x} & \color{blue}{-9} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-16x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{-18x} & \color{blue}{-9} \\ \hline \color{blue}{2x^2} & \color{orangered}{6x^4} & \color{orangered}{-36x^3} & \color{orangered}{-18x^2} \\ \hline \color{blue}{-16x} & \color{orangered}{-48x^3} & \color{orangered}{288x^2} & \color{orangered}{144x} \\ \hline \color{blue}{2} & \color{orangered}{6x^2} & \color{orangered}{-36x} & \color{orangered}{-18} \\ \hline \end{darray} $$

Combine like terms:

$$ 6x^4-36x^3-48x^3-18x^2 + 288x^2 + 6x^2 + 144x-36x-18 = \\ 6x^4-84x^3+276x^2+108x-18 $$

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