We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{2x^2} & \color{blue}{x} & \color{blue}{1} \\ \hline \color{blue}{x} & & & & \\ \hline \color{blue}{1} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{x^3} & \color{blue}{2x^2} & \color{blue}{x} & \color{blue}{1} \\ \hline \color{blue}{x} & \color{orangered}{x^4} & \color{orangered}{2x^3} & \color{orangered}{x^2} & \color{orangered}{x} \\ \hline \color{blue}{1} & \color{orangered}{x^3} & \color{orangered}{2x^2} & \color{orangered}{x} & \color{orangered}{1} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4 + 2x^3 + x^3 + x^2 + 2x^2 + x + x + 1 = \\ x^4+3x^3+3x^2+2x+1 $$

Polynomial Operations Calculator