We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{10x} & \color{blue}{26} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-19x} & & & \\ \hline \color{blue}{18} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{10x} & \color{blue}{26} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{10x^3} & \color{orangered}{26x^2} \\ \hline \color{blue}{-19x} & \color{orangered}{-19x^3} & \color{orangered}{-190x^2} & \color{orangered}{-494x} \\ \hline \color{blue}{18} & \color{orangered}{18x^2} & \color{orangered}{180x} & \color{orangered}{468} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 10x^3-19x^3 + 26x^2-190x^2 + 18x^2-494x + 180x + 468 = \\ x^4-9x^3-146x^2-314x+468 $$

Polynomial Operations Calculator