We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7x^3} & \color{blue}{-6x^2} & \color{blue}{8} \\ \hline \color{blue}{8x^3} & & & \\ \hline \color{blue}{8x^2} & & & \\ \hline \color{blue}{16} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{7x^3} & \color{blue}{-6x^2} & \color{blue}{8} \\ \hline \color{blue}{8x^3} & \color{orangered}{56x^6} & \color{orangered}{-48x^5} & \color{orangered}{64x^3} \\ \hline \color{blue}{8x^2} & \color{orangered}{56x^5} & \color{orangered}{-48x^4} & \color{orangered}{64x^2} \\ \hline \color{blue}{16} & \color{orangered}{112x^3} & \color{orangered}{-96x^2} & \color{orangered}{128} \\ \hline \end{darray} $$

Combine like terms:

$$ 56x^6-48x^5 + 56x^5 + 64x^3-48x^4 + 112x^3 + 64x^2-96x^2 + 128 = \\ 56x^6+8x^5-48x^4+176x^3-32x^2+128 $$

Polynomial Operations Calculator