Multiply polynomial $ \, \color{blue}{ 2x^2-x-2 } \, $ by $ \, \color{orangered}{ -2x^2-3x+8 }$.

$$ \left( \color{blue}{2x^2-x-2} \right) \cdot \left( \color{orangered}{-2x^2-3x+8} \right) = -4x^4-4x^3+23x^2-2x-16 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-x} & \color{blue}{-2} \\ \hline \color{blue}{-2x^2} & & & \\ \hline \color{blue}{-3x} & & & \\ \hline \color{blue}{8} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{-x} & \color{blue}{-2} \\ \hline \color{blue}{-2x^2} & \color{orangered}{-4x^4} & \color{orangered}{2x^3} & \color{orangered}{4x^2} \\ \hline \color{blue}{-3x} & \color{orangered}{-6x^3} & \color{orangered}{3x^2} & \color{orangered}{6x} \\ \hline \color{blue}{8} & \color{orangered}{16x^2} & \color{orangered}{-8x} & \color{orangered}{-16} \\ \hline \end{darray} $$

Combine like terms:

$$ -4x^4 + 2x^3-6x^3 + 4x^2 + 3x^2 + 16x^2 + 6x-8x-16 = \\ -4x^4-4x^3+23x^2-2x-16 $$

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