We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

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

Combine like terms:

$$ x^4-3x^3 + 3x^3-2x^2-9x^2-7x^2-6x + 21x + 14 = \\ x^4-18x^2+15x+14 $$

Polynomial Operations Calculator