We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{9x} & \color{blue}{7} \\ \hline \color{blue}{3x^2} & & & \\ \hline \color{blue}{9x} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{9x} & \color{blue}{7} \\ \hline \color{blue}{3x^2} & \color{orangered}{3x^4} & \color{orangered}{27x^3} & \color{orangered}{21x^2} \\ \hline \color{blue}{9x} & \color{orangered}{9x^3} & \color{orangered}{81x^2} & \color{orangered}{63x} \\ \hline \color{blue}{5} & \color{orangered}{5x^2} & \color{orangered}{45x} & \color{orangered}{35} \\ \hline \end{darray} $$

Combine like terms:

$$ 3x^4 + 27x^3 + 9x^3 + 21x^2 + 81x^2 + 5x^2 + 63x + 45x + 35 = \\ 3x^4+36x^3+107x^2+108x+35 $$

Polynomial Operations Calculator