We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{-4x^3} & \color{blue}{-5x^2} & \color{blue}{14x} & \color{blue}{-6} \\ \hline \color{blue}{4x} & & & & \\ \hline \color{blue}{-3} & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|}\hline & \color{blue}{-4x^3} & \color{blue}{-5x^2} & \color{blue}{14x} & \color{blue}{-6} \\ \hline \color{blue}{4x} & \color{orangered}{-16x^4} & \color{orangered}{-20x^3} & \color{orangered}{56x^2} & \color{orangered}{-24x} \\ \hline \color{blue}{-3} & \color{orangered}{12x^3} & \color{orangered}{15x^2} & \color{orangered}{-42x} & \color{orangered}{18} \\ \hline \end{darray} $$

Combine like terms:

$$ -16x^4-20x^3 + 12x^3 + 56x^2 + 15x^2-24x-42x + 18 = \\ -16x^4-8x^3+71x^2-66x+18 $$

Polynomial Operations Calculator