Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -5y+2 \\ Q(x) &= y^2+6y+9 \\ \end{aligned} $$

We can multiply polynomials by using a GRID METHOD

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

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{6y} & \color{blue}{9} \\ \hline \color{blue}{-5y} & & & \\ \hline \color{blue}{2} & & & \\ \hline \end{darray} $$

Fill in each empty box by multiplying the intersecting terms.

$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{6y} & \color{blue}{9} \\ \hline \color{blue}{-5y} & \color{orangered}{-5y^3} & \color{orangered}{-30y^2} & \color{orangered}{-45y} \\ \hline \color{blue}{2} & \color{orangered}{2y^2} & \color{orangered}{12y} & \color{orangered}{18} \\ \hline \end{darray} $$

Combine like terms:

$$ -5y^3-30y^2 + 2y^2-45y + 12y + 18 = \\ -5y^3-28y^2-33y+18 $$

Polynomial Operations Calculator