Question
Multiply polynomial $ \, \color{blue}{ 5y^2-9y-2 } \, $ by $ \, \color{orangered}{ y-2 }$.
Answer
$$ \left( \color{blue}{5y^2-9y-2} \right) \cdot \left( \color{orangered}{y-2} \right) = 5y^3-19y^2+16y+4 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5y^2} & \color{blue}{-9y} & \color{blue}{-2} \\ \hline \color{blue}{y} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5y^2} & \color{blue}{-9y} & \color{blue}{-2} \\ \hline \color{blue}{y} & \color{orangered}{5y^3} & \color{orangered}{-9y^2} & \color{orangered}{-2y} \\ \hline \color{blue}{-2} & \color{orangered}{-10y^2} & \color{orangered}{18y} & \color{orangered}{4} \\ \hline \end{darray} $$Combine like terms:
$$ 5y^3-9y^2-10y^2-2y + 18y + 4 = \\ 5y^3-19y^2+16y+4 $$This page was created using
Polynomial Operations Calculator