We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ 2x^4 + 5x^3 + 4x^3 + 2x^2 + 10x^2-6x^2 + 4x-15x-6 = \\ 2x^4+9x^3+6x^2-11x-6 $$

Polynomial Operations Calculator