Question
Multiply polynomial $ \, \color{blue}{ 3y^2-3y-3 } \, $ by $ \, \color{orangered}{ 2y-3 }$.
Answer
$$ \left( \color{blue}{3y^2-3y-3} \right) \cdot \left( \color{orangered}{2y-3} \right) = 6y^3-15y^2+3y+9 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3y^2} & \color{blue}{-3y} & \color{blue}{-3} \\ \hline \color{blue}{2y} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3y^2} & \color{blue}{-3y} & \color{blue}{-3} \\ \hline \color{blue}{2y} & \color{orangered}{6y^3} & \color{orangered}{-6y^2} & \color{orangered}{-6y} \\ \hline \color{blue}{-3} & \color{orangered}{-9y^2} & \color{orangered}{9y} & \color{orangered}{9} \\ \hline \end{darray} $$Combine like terms:
$$ 6y^3-6y^2-9y^2-6y + 9y + 9 = \\ 6y^3-15y^2+3y+9 $$This page was created using
Polynomial Operations Calculator