Question
Multiply polynomial $ \, \color{blue}{ 8b-2 } \, $ by $ \, \color{orangered}{ 3b^2+2b-2 }$.
Answer
$$ \left( \color{blue}{8b-2} \right) \cdot \left( \color{orangered}{3b^2+2b-2} \right) = 24b^3+10b^2-20b+4 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3b^2} & \color{blue}{2b} & \color{blue}{-2} \\ \hline \color{blue}{8b} & & & \\ \hline \color{blue}{-2} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{3b^2} & \color{blue}{2b} & \color{blue}{-2} \\ \hline \color{blue}{8b} & \color{orangered}{24b^3} & \color{orangered}{16b^2} & \color{orangered}{-16b} \\ \hline \color{blue}{-2} & \color{orangered}{-6b^2} & \color{orangered}{-4b} & \color{orangered}{4} \\ \hline \end{darray} $$Combine like terms:
$$ 24b^3 + 16b^2-6b^2-16b-4b + 4 = \\ 24b^3+10b^2-20b+4 $$This page was created using
Polynomial Operations Calculator