Multiply polynomial $ \, \color{blue}{ x^2+6x+9 } \, $ by $ \, \color{orangered}{ x+3 }$.

$$ \left( \color{blue}{x^2+6x+9} \right) \cdot \left( \color{orangered}{x+3} \right) = x^3+9x^2+27x+27 $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{6x} & \color{blue}{9} \\ \hline \color{blue}{x} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{6x} & \color{blue}{9} \\ \hline \color{blue}{x} & \color{orangered}{x^3} & \color{orangered}{6x^2} & \color{orangered}{9x} \\ \hline \color{blue}{3} & \color{orangered}{3x^2} & \color{orangered}{18x} & \color{orangered}{27} \\ \hline \end{darray} $$

Combine like terms:

$$ x^3 + 6x^2 + 3x^2 + 9x + 18x + 27 = \\ x^3+9x^2+27x+27 $$

Polynomial Operations Calculator