Multiply polynomial $ \, \color{blue}{ x^2-6x-40 } \, $ by $ \, \color{orangered}{ x-10 }$.

$$ \left( \color{blue}{x^2-6x-40} \right) \cdot \left( \color{orangered}{x-10} \right) = x^3-16x^2+20x+400 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{-40} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-10} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{-40} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-6x^2} & \color{orangered}{-40x} \\ \hline \color{blue}{-10} & \color{orangered}{-10x^2} & \color{orangered}{60x} & \color{orangered}{400} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3-6x^2-10x^2-40x + 60x + 400 = \\ x^3-16x^2+20x+400 $$

Polynomial Operations Calculator