Multiply polynomial $ \, \color{blue}{ 6c^5-2c^4-2 } \, $ by $ \, \color{orangered}{ -11c^2-15 }$.

$$ \left( \color{blue}{6c^5-2c^4-2} \right) \cdot \left( \color{orangered}{-11c^2-15} \right) = -66c^7+22c^6-90c^5+30c^4+22c^2+30 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6c^5} & \color{blue}{-2c^4} & \color{blue}{-2} \\ \hline \color{blue}{-11c^2} & & & \\ \hline \color{blue}{-15} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6c^5} & \color{blue}{-2c^4} & \color{blue}{-2} \\ \hline \color{blue}{-11c^2} & \color{orangered}{-66c^7} & \color{orangered}{22c^6} & \color{orangered}{22c^2} \\ \hline \color{blue}{-15} & \color{orangered}{-90c^5} & \color{orangered}{30c^4} & \color{orangered}{30} \\ \hline \end{darray} $$

Combine like terms:

$$ -66c^7 + 22c^6-90c^5 + 22c^2 + 30c^4 + 30 = \\ -66c^7+22c^6-90c^5+30c^4+22c^2+30 $$

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