We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{1} \\ \hline \color{blue}{4x^2} & & & \\ \hline \color{blue}{28x} & & & \\ \hline \color{blue}{49} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{2x} & \color{blue}{1} \\ \hline \color{blue}{4x^2} & \color{orangered}{4x^4} & \color{orangered}{8x^3} & \color{orangered}{4x^2} \\ \hline \color{blue}{28x} & \color{orangered}{28x^3} & \color{orangered}{56x^2} & \color{orangered}{28x} \\ \hline \color{blue}{49} & \color{orangered}{49x^2} & \color{orangered}{98x} & \color{orangered}{49} \\ \hline \end{darray} $$

Combine like terms:

$$ 4x^4 + 8x^3 + 28x^3 + 4x^2 + 56x^2 + 49x^2 + 28x + 98x + 49 = \\ 4x^4+36x^3+109x^2+126x+49 $$

Polynomial Operations Calculator