We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-2x} & \color{blue}{-3} \\ \hline \color{blue}{7x^2} & & & \\ \hline \color{blue}{-3x} & & & \\ \hline \color{blue}{13} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^3} & \color{blue}{-2x} & \color{blue}{-3} \\ \hline \color{blue}{7x^2} & \color{orangered}{14x^5} & \color{orangered}{-14x^3} & \color{orangered}{-21x^2} \\ \hline \color{blue}{-3x} & \color{orangered}{-6x^4} & \color{orangered}{6x^2} & \color{orangered}{9x} \\ \hline \color{blue}{13} & \color{orangered}{26x^3} & \color{orangered}{-26x} & \color{orangered}{-39} \\ \hline \end{darray} $$

Combine like terms:

$$ 14x^5-14x^3-6x^4-21x^2 + 6x^2 + 26x^3 + 9x-26x-39 = \\ 14x^5-6x^4+12x^3-15x^2-17x-39 $$

Polynomial Operations Calculator