Question
Multiply polynomial $ \, \color{blue}{ -3n+5 } \, $ by $ \, \color{orangered}{ 2n^2-4n-7 }$.
Answer
$$ \left( \color{blue}{-3n+5} \right) \cdot \left( \color{orangered}{2n^2-4n-7} \right) = -6n^3+22n^2+n-35 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2n^2} & \color{blue}{-4n} & \color{blue}{-7} \\ \hline \color{blue}{-3n} & & & \\ \hline \color{blue}{5} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2n^2} & \color{blue}{-4n} & \color{blue}{-7} \\ \hline \color{blue}{-3n} & \color{orangered}{-6n^3} & \color{orangered}{12n^2} & \color{orangered}{21n} \\ \hline \color{blue}{5} & \color{orangered}{10n^2} & \color{orangered}{-20n} & \color{orangered}{-35} \\ \hline \end{darray} $$Combine like terms:
$$ -6n^3 + 12n^2 + 10n^2 + 21n-20n-35 = \\ -6n^3+22n^2+n-35 $$This page was created using
Polynomial Operations Calculator