We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{-12x^2} & \color{blue}{-33x} & \color{blue}{-35} \\ \hline \color{blue}{x} & & & & \\ \hline \color{blue}{3} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{4x^3} & \color{blue}{-12x^2} & \color{blue}{-33x} & \color{blue}{-35} \\ \hline \color{blue}{x} & \color{orangered}{4x^4} & \color{orangered}{-12x^3} & \color{orangered}{-33x^2} & \color{orangered}{-35x} \\ \hline \color{blue}{3} & \color{orangered}{12x^3} & \color{orangered}{-36x^2} & \color{orangered}{-99x} & \color{orangered}{-105} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^4-12x^3 + 12x^3-33x^2-36x^2-35x-99x-105 = \\ 4x^4-69x^2-134x-105 $$

Polynomial Operations Calculator