We can multiply polynomials by using a GRID METHOD

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

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

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2x^2} & \color{blue}{9x} & \color{blue}{7} \\ \hline \color{blue}{2x^2} & \color{orangered}{4x^4} & \color{orangered}{18x^3} & \color{orangered}{14x^2} \\ \hline \color{blue}{9x} & \color{orangered}{18x^3} & \color{orangered}{81x^2} & \color{orangered}{63x} \\ \hline \color{blue}{7} & \color{orangered}{14x^2} & \color{orangered}{63x} & \color{orangered}{49} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^4 + 18x^3 + 18x^3 + 14x^2 + 81x^2 + 14x^2 + 63x + 63x + 49 = \\ 4x^4+36x^3+109x^2+126x+49 $$

Polynomial Operations Calculator