Question
Multiply polynomial $ \, \color{blue}{ 2n^2-5n-5 } \, $ by $ \, \color{orangered}{ 3n-3 }$.
Answer
$$ \left( \color{blue}{2n^2-5n-5} \right) \cdot \left( \color{orangered}{3n-3} \right) = 6n^3-21n^2+15 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2n^2} & \color{blue}{-5n} & \color{blue}{-5} \\ \hline \color{blue}{3n} & & & \\ \hline \color{blue}{-3} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{2n^2} & \color{blue}{-5n} & \color{blue}{-5} \\ \hline \color{blue}{3n} & \color{orangered}{6n^3} & \color{orangered}{-15n^2} & \color{orangered}{-15n} \\ \hline \color{blue}{-3} & \color{orangered}{-6n^2} & \color{orangered}{15n} & \color{orangered}{15} \\ \hline \end{darray} $$Combine like terms:
$$ 6n^3-15n^2-6n^2-15n + 15n + 15 = \\ 6n^3-21n^2+15 $$This page was created using
Polynomial Operations Calculator