We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{3} \\ \hline \color{blue}{2x^2} & & & \\ \hline \color{blue}{-16x} & & & \\ \hline \color{blue}{30} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{4x} & \color{blue}{3} \\ \hline \color{blue}{2x^2} & \color{orangered}{2x^4} & \color{orangered}{8x^3} & \color{orangered}{6x^2} \\ \hline \color{blue}{-16x} & \color{orangered}{-16x^3} & \color{orangered}{-64x^2} & \color{orangered}{-48x} \\ \hline \color{blue}{30} & \color{orangered}{30x^2} & \color{orangered}{120x} & \color{orangered}{90} \\ \hline \end{darray} $$

Combine like terms:

$$ 2x^4 + 8x^3-16x^3 + 6x^2-64x^2 + 30x^2-48x + 120x + 90 = \\ 2x^4-8x^3-28x^2+72x+90 $$

Polynomial Operations Calculator