Multiply polynomial $ \, \color{blue}{ 6x^2+6x-2 } \, $ by $ \, \color{orangered}{ 3x^2-6x+4 }$.

$$ \left( \color{blue}{6x^2+6x-2} \right) \cdot \left( \color{orangered}{3x^2-6x+4} \right) = 18x^4-18x^3-18x^2+36x-8 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{6x} & \color{blue}{-2} \\ \hline \color{blue}{3x^2} & & & \\ \hline \color{blue}{-6x} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{6x^2} & \color{blue}{6x} & \color{blue}{-2} \\ \hline \color{blue}{3x^2} & \color{orangered}{18x^4} & \color{orangered}{18x^3} & \color{orangered}{-6x^2} \\ \hline \color{blue}{-6x} & \color{orangered}{-36x^3} & \color{orangered}{-36x^2} & \color{orangered}{12x} \\ \hline \color{blue}{4} & \color{orangered}{24x^2} & \color{orangered}{24x} & \color{orangered}{-8} \\ \hline \end{darray} $$

Combine like terms:

$$ 18x^4 + 18x^3-36x^3-6x^2-36x^2 + 24x^2 + 12x + 24x-8 = \\ 18x^4-18x^3-18x^2+36x-8 $$

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