Multiply polynomial $ \, \color{blue}{ x^2-6x+13 } \, $ by $ \, \color{orangered}{ x^2-8x+15 }$.

$$ \left( \color{blue}{x^2-6x+13} \right) \cdot \left( \color{orangered}{x^2-8x+15} \right) = x^4-14x^3+76x^2-194x+195 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{13} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-8x} & & & \\ \hline \color{blue}{15} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{13} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-6x^3} & \color{orangered}{13x^2} \\ \hline \color{blue}{-8x} & \color{orangered}{-8x^3} & \color{orangered}{48x^2} & \color{orangered}{-104x} \\ \hline \color{blue}{15} & \color{orangered}{15x^2} & \color{orangered}{-90x} & \color{orangered}{195} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4-6x^3-8x^3 + 13x^2 + 48x^2 + 15x^2-104x-90x + 195 = \\ x^4-14x^3+76x^2-194x+195 $$

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