Question
Multiply polynomial $ \, \color{blue}{ 4b+1 } \, $ by $ \, \color{orangered}{ -3b^2+4b+1 }$.
Answer
$$ \left( \color{blue}{4b+1} \right) \cdot \left( \color{orangered}{-3b^2+4b+1} \right) = -12b^3+13b^2+8b+1 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3b^2} & \color{blue}{4b} & \color{blue}{1} \\ \hline \color{blue}{4b} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{-3b^2} & \color{blue}{4b} & \color{blue}{1} \\ \hline \color{blue}{4b} & \color{orangered}{-12b^3} & \color{orangered}{16b^2} & \color{orangered}{4b} \\ \hline \color{blue}{1} & \color{orangered}{-3b^2} & \color{orangered}{4b} & \color{orangered}{1} \\ \hline \end{darray} $$Combine like terms:
$$ -12b^3 + 16b^2-3b^2 + 4b + 4b + 1 = \\ -12b^3+13b^2+8b+1 $$This page was created using
Polynomial Operations Calculator