We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{-5x} & \color{blue}{-1} \\ \hline \color{blue}{4x^2} & & & \\ \hline \color{blue}{-6x} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-4x^2} & \color{blue}{-5x} & \color{blue}{-1} \\ \hline \color{blue}{4x^2} & \color{orangered}{-16x^4} & \color{orangered}{-20x^3} & \color{orangered}{-4x^2} \\ \hline \color{blue}{-6x} & \color{orangered}{24x^3} & \color{orangered}{30x^2} & \color{orangered}{6x} \\ \hline \color{blue}{-2} & \color{orangered}{8x^2} & \color{orangered}{10x} & \color{orangered}{2} \\ \hline \end{darray} $$

Combine like terms:

$$ -16x^4-20x^3 + 24x^3-4x^2 + 30x^2 + 8x^2 + 6x + 10x + 2 = \\ -16x^4+4x^3+34x^2+16x+2 $$

Polynomial Operations Calculator