Question
Multiply polynomial $ \, \color{blue}{ -3y+1 } \, $ by $ \, \color{orangered}{ 4y^2-y-7 }$.
Answer
$$ \left( \color{blue}{-3y+1} \right) \cdot \left( \color{orangered}{4y^2-y-7} \right) = -12y^3+7y^2+20y-7 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4y^2} & \color{blue}{-y} & \color{blue}{-7} \\ \hline \color{blue}{-3y} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{4y^2} & \color{blue}{-y} & \color{blue}{-7} \\ \hline \color{blue}{-3y} & \color{orangered}{-12y^3} & \color{orangered}{3y^2} & \color{orangered}{21y} \\ \hline \color{blue}{1} & \color{orangered}{4y^2} & \color{orangered}{-y} & \color{orangered}{-7} \\ \hline \end{darray} $$Combine like terms:
$$ -12y^3 + 3y^2 + 4y^2 + 21y-y-7 = \\ -12y^3+7y^2+20y-7 $$This page was created using
Polynomial Operations Calculator