Multiply polynomial $ \, \color{blue}{ y^2+2y } \, $ by $ \, \color{orangered}{ y^2+5y+8 }$.

$$ \left( \color{blue}{y^2+2y} \right) \cdot \left( \color{orangered}{y^2+5y+8} \right) = y^4+7y^3+18y^2+16y $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{5y} & \color{blue}{8} \\ \hline \color{blue}{y^2} & & & \\ \hline \color{blue}{2y} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{5y} & \color{blue}{8} \\ \hline \color{blue}{y^2} & \color{orangered}{y^4} & \color{orangered}{5y^3} & \color{orangered}{8y^2} \\ \hline \color{blue}{2y} & \color{orangered}{2y^3} & \color{orangered}{10y^2} & \color{orangered}{16y} \\ \hline \end{darray} $$

Combine like terms:

$$ y^4 + 5y^3 + 2y^3 + 8y^2 + 10y^2 + 16y = \\ y^4+7y^3+18y^2+16y $$

Polynomial Operations Calculator