We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5y^2} & \color{blue}{-5y} & \color{blue}{2} \\ \hline \color{blue}{2y^2} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5y^2} & \color{blue}{-5y} & \color{blue}{2} \\ \hline \color{blue}{2y^2} & \color{orangered}{10y^4} & \color{orangered}{-10y^3} & \color{orangered}{4y^2} \\ \hline \color{blue}{-2} & \color{orangered}{-10y^2} & \color{orangered}{10y} & \color{orangered}{-4} \\ \hline \end{darray} $$Combine like terms:
$$ 10y^4-10y^3-10y^2 + 4y^2 + 10y-4 = \\ 10y^4-10y^3-6y^2+10y-4 $$