Question
Multiply polynomial $ \, \color{blue}{ y^2+6y+9 } \, $ by $ \, \color{orangered}{ y+3 }$.
Answer
$$ \left( \color{blue}{y^2+6y+9} \right) \cdot \left( \color{orangered}{y+3} \right) = y^3+9y^2+27y+27 $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{6y} & \color{blue}{9} \\ \hline \color{blue}{y} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{6y} & \color{blue}{9} \\ \hline \color{blue}{y} & \color{orangered}{y^3} & \color{orangered}{6y^2} & \color{orangered}{9y} \\ \hline \color{blue}{3} & \color{orangered}{3y^2} & \color{orangered}{18y} & \color{orangered}{27} \\ \hline \end{darray} $$Combine like terms:
$$ y^3 + 6y^2 + 3y^2 + 9y + 18y + 27 = \\ y^3+9y^2+27y+27 $$This page was created using
Polynomial Operations Calculator