Multiply polynomial $ \, \color{blue}{ -3x^2-4x+7 } \, $ by $ \, \color{orangered}{ 2x^2-4x+4 }$.

$$ \left( \color{blue}{-3x^2-4x+7} \right) \cdot \left( \color{orangered}{2x^2-4x+4} \right) = -6x^4+4x^3+18x^2-44x+28 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3x^2} & \color{blue}{-4x} & \color{blue}{7} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-4x} & & & \\ \hline \color{blue}{4} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3x^2} & \color{blue}{-4x} & \color{blue}{7} \\ \hline \color{blue}{2x^2} & \color{orangered}{-6x^4} & \color{orangered}{-8x^3} & \color{orangered}{14x^2} \\ \hline \color{blue}{-4x} & \color{orangered}{12x^3} & \color{orangered}{16x^2} & \color{orangered}{-28x} \\ \hline \color{blue}{4} & \color{orangered}{-12x^2} & \color{orangered}{-16x} & \color{orangered}{28} \\ \hline \end{darray} $$

Combine like terms:

$$ -6x^4-8x^3 + 12x^3 + 14x^2 + 16x^2-12x^2-28x-16x + 28 = \\ -6x^4+4x^3+18x^2-44x+28 $$

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