We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{7x} & \color{blue}{-4} \\ \hline \color{blue}{8x^2} & & & \\ \hline \color{blue}{-6x} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3x^2} & \color{blue}{7x} & \color{blue}{-4} \\ \hline \color{blue}{8x^2} & \color{orangered}{24x^4} & \color{orangered}{56x^3} & \color{orangered}{-32x^2} \\ \hline \color{blue}{-6x} & \color{orangered}{-18x^3} & \color{orangered}{-42x^2} & \color{orangered}{24x} \\ \hline \color{blue}{2} & \color{orangered}{6x^2} & \color{orangered}{14x} & \color{orangered}{-8} \\ \hline \end{darray} $$

Combine like terms:

$$ 24x^4 + 56x^3-18x^3-32x^2-42x^2 + 6x^2 + 24x + 14x-8 = \\ 24x^4+38x^3-68x^2+38x-8 $$

Polynomial Operations Calculator