Question
Multiply polynomial $ \, \color{blue}{ y+3 } \, $ by $ \, \color{orangered}{ 2y^2-3y-4 }$.
Answer
$$ \left( \color{blue}{y+3} \right) \cdot \left( \color{orangered}{2y^2-3y-4} \right) = 2y^3+3y^2-13y-12 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2y^2} & \color{blue}{-3y} & \color{blue}{-4} \\ \hline \color{blue}{y} & & & \\ \hline \color{blue}{3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2y^2} & \color{blue}{-3y} & \color{blue}{-4} \\ \hline \color{blue}{y} & \color{orangered}{2y^3} & \color{orangered}{-3y^2} & \color{orangered}{-4y} \\ \hline \color{blue}{3} & \color{orangered}{6y^2} & \color{orangered}{-9y} & \color{orangered}{-12} \\ \hline \end{darray} $$Combine like terms:
$$ 2y^3-3y^2 + 6y^2-4y-9y-12 = \\ 2y^3+3y^2-13y-12 $$This page was created using
Polynomial Operations Calculator