We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-4x} & \color{blue}{4} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-4x^3} & \color{orangered}{4x^2} \\ \hline \color{blue}{4x} & \color{orangered}{4x^3} & \color{orangered}{-16x^2} & \color{orangered}{16x} \\ \hline \color{blue}{4} & \color{orangered}{4x^2} & \color{orangered}{-16x} & \color{orangered}{16} \\ \hline \end{darray} $$

Combine like terms:

$$ x^4-4x^3 + 4x^3 + 4x^2-16x^2 + 4x^2 + 16x-16x + 16 = \\ x^4-8x^2+16 $$

Polynomial Operations Calculator