Question
Multiply polynomial $ \, \color{blue}{ y-1 } \, $ by $ \, \color{orangered}{ y^2-7y+2 }$.
Answer
$$ \left( \color{blue}{y-1} \right) \cdot \left( \color{orangered}{y^2-7y+2} \right) = y^3-8y^2+9y-2 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{-7y} & \color{blue}{2} \\ \hline \color{blue}{y} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{y^2} & \color{blue}{-7y} & \color{blue}{2} \\ \hline \color{blue}{y} & \color{orangered}{y^3} & \color{orangered}{-7y^2} & \color{orangered}{2y} \\ \hline \color{blue}{-1} & \color{orangered}{-y^2} & \color{orangered}{7y} & \color{orangered}{-2} \\ \hline \end{darray} $$Combine like terms:
$$ y^3-7y^2-y^2 + 2y + 7y-2 = \\ y^3-8y^2+9y-2 $$This page was created using
Polynomial Operations Calculator