We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{22x^2} & \color{blue}{105x} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{19x} & & & \\ \hline \color{blue}{90} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{22x^2} & \color{blue}{105x} \\ \hline \color{blue}{x^2} & \color{orangered}{x^5} & \color{orangered}{22x^4} & \color{orangered}{105x^3} \\ \hline \color{blue}{19x} & \color{orangered}{19x^4} & \color{orangered}{418x^3} & \color{orangered}{1995x^2} \\ \hline \color{blue}{90} & \color{orangered}{90x^3} & \color{orangered}{1980x^2} & \color{orangered}{9450x} \\ \hline \end{darray} $$

Combine like terms:

$$ x^5 + 22x^4 + 19x^4 + 105x^3 + 418x^3 + 90x^3 + 1995x^2 + 1980x^2 + 9450x = \\ x^5+41x^4+613x^3+3975x^2+9450x $$

Polynomial Operations Calculator