We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|c|}\hline & \color{blue}{2x^5} & \color{blue}{x^4} & \color{blue}{x^3} & \color{blue}{-2x} & \color{blue}{-3} \\ \hline \color{blue}{2x} & \color{orangered}{4x^6} & \color{orangered}{2x^5} & \color{orangered}{2x^4} & \color{orangered}{-4x^2} & \color{orangered}{-6x} \\ \hline \color{blue}{5} & \color{orangered}{10x^5} & \color{orangered}{5x^4} & \color{orangered}{5x^3} & \color{orangered}{-10x} & \color{orangered}{-15} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^6 + 2x^5 + 10x^5 + 2x^4 + 5x^4-4x^2 + 5x^3-6x-10x-15 = \\ 4x^6+12x^5+7x^4+5x^3-4x^2-16x-15 $$

Polynomial Operations Calculator