We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|c|c|}\hline & \color{blue}{x^5} & \color{blue}{6x^4} & \color{blue}{-3x^2} & \color{blue}{-22x} & \color{blue}{-29} \\ \hline \color{blue}{x} & & & & & \\ \hline \color{blue}{6} & & & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|c|c|}\hline & \color{blue}{x^5} & \color{blue}{6x^4} & \color{blue}{-3x^2} & \color{blue}{-22x} & \color{blue}{-29} \\ \hline \color{blue}{x} & \color{orangered}{x^6} & \color{orangered}{6x^5} & \color{orangered}{-3x^3} & \color{orangered}{-22x^2} & \color{orangered}{-29x} \\ \hline \color{blue}{6} & \color{orangered}{6x^5} & \color{orangered}{36x^4} & \color{orangered}{-18x^2} & \color{orangered}{-132x} & \color{orangered}{-174} \\ \hline \end{darray} $$

Combine like terms:

$$ x^6 + 6x^5 + 6x^5-3x^3 + 36x^4-22x^2-18x^2-29x-132x-174 = \\ x^6+12x^5+36x^4-3x^3-40x^2-161x-174 $$

Polynomial Operations Calculator