Multiply polynomial $ \, \color{blue}{ x^2-9x-10 } \, $ by $ \, \color{orangered}{ x-10 }$.

$$ \left( \color{blue}{x^2-9x-10} \right) \cdot \left( \color{orangered}{x-10} \right) = x^3-19x^2+80x+100 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-9x} & \color{blue}{-10} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{-10} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-9x} & \color{blue}{-10} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{-9x^2} & \color{orangered}{-10x} \\ \hline \color{blue}{-10} & \color{orangered}{-10x^2} & \color{orangered}{90x} & \color{orangered}{100} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3-9x^2-10x^2-10x + 90x + 100 = \\ x^3-19x^2+80x+100 $$

Polynomial Operations Calculator