We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ x^4-2x^3 + 5x^3 + 2x^2-10x^2-6x^2 + 10x + 12x-12 = \\ x^4+3x^3-14x^2+22x-12 $$

Polynomial Operations Calculator