Question
Multiply polynomial $ \, \color{blue}{ 5b-6 } \, $ by $ \, \color{orangered}{ 5b^2+4b-2 }$.
Answer
$$ \left( \color{blue}{5b-6} \right) \cdot \left( \color{orangered}{5b^2+4b-2} \right) = 25b^3-10b^2-34b+12 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5b^2} & \color{blue}{4b} & \color{blue}{-2} \\ \hline \color{blue}{5b} & & & \\ \hline \color{blue}{-6} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{5b^2} & \color{blue}{4b} & \color{blue}{-2} \\ \hline \color{blue}{5b} & \color{orangered}{25b^3} & \color{orangered}{20b^2} & \color{orangered}{-10b} \\ \hline \color{blue}{-6} & \color{orangered}{-30b^2} & \color{orangered}{-24b} & \color{orangered}{12} \\ \hline \end{darray} $$Combine like terms:
$$ 25b^3 + 20b^2-30b^2-10b-24b + 12 = \\ 25b^3-10b^2-34b+12 $$This page was created using
Polynomial Operations Calculator