Question
Multiply polynomial $ \, \color{blue}{ -3b^2+4b+5 } \, $ by $ \, \color{orangered}{ -2b-1 }$.
Answer
$$ \left( \color{blue}{-3b^2+4b+5} \right) \cdot \left( \color{orangered}{-2b-1} \right) = 6b^3-5b^2-14b-5 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3b^2} & \color{blue}{4b} & \color{blue}{5} \\ \hline \color{blue}{-2b} & & & \\ \hline \color{blue}{-1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3b^2} & \color{blue}{4b} & \color{blue}{5} \\ \hline \color{blue}{-2b} & \color{orangered}{6b^3} & \color{orangered}{-8b^2} & \color{orangered}{-10b} \\ \hline \color{blue}{-1} & \color{orangered}{3b^2} & \color{orangered}{-4b} & \color{orangered}{-5} \\ \hline \end{darray} $$Combine like terms:
$$ 6b^3-8b^2 + 3b^2-10b-4b-5 = \\ 6b^3-5b^2-14b-5 $$This page was created using
Polynomial Operations Calculator