We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{2x} & \color{blue}{-3} \\ \hline \color{blue}{5x^2} & \color{orangered}{10x^4} & \color{orangered}{10x^3} & \color{orangered}{-15x^2} \\ \hline \color{blue}{5x} & \color{orangered}{10x^3} & \color{orangered}{10x^2} & \color{orangered}{-15x} \\ \hline \color{blue}{-6} & \color{orangered}{-12x^2} & \color{orangered}{-12x} & \color{orangered}{18} \\ \hline \end{darray} $$

Combine like terms:

$$ 10x^4 + 10x^3 + 10x^3-15x^2 + 10x^2-12x^2-15x-12x + 18 = \\ 10x^4+20x^3-17x^2-27x+18 $$

Polynomial Operations Calculator