Multiply polynomial $ \, \color{blue}{ 7x^2+8x+2 } \, $ by $ \, \color{orangered}{ 4x^2-6x-2 }$.

$$ \left( \color{blue}{7x^2+8x+2} \right) \cdot \left( \color{orangered}{4x^2-6x-2} \right) = 28x^4-10x^3-54x^2-28x-4 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7x^2} & \color{blue}{8x} & \color{blue}{2} \\ \hline \color{blue}{4x^2} & & & \\ \hline \color{blue}{-6x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7x^2} & \color{blue}{8x} & \color{blue}{2} \\ \hline \color{blue}{4x^2} & \color{orangered}{28x^4} & \color{orangered}{32x^3} & \color{orangered}{8x^2} \\ \hline \color{blue}{-6x} & \color{orangered}{-42x^3} & \color{orangered}{-48x^2} & \color{orangered}{-12x} \\ \hline \color{blue}{-2} & \color{orangered}{-14x^2} & \color{orangered}{-16x} & \color{orangered}{-4} \\ \hline \end{darray} $$

Combine like terms:

$$ 28x^4 + 32x^3-42x^3 + 8x^2-48x^2-14x^2-12x-16x-4 = \\ 28x^4-10x^3-54x^2-28x-4 $$

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