Question
Multiply polynomial $ \, \color{blue}{ t^2+7t+6 } \, $ by $ \, \color{orangered}{ 2t+1 }$.
Answer
$$ \left( \color{blue}{t^2+7t+6} \right) \cdot \left( \color{orangered}{2t+1} \right) = 2t^3+15t^2+19t+6 $$
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.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{t^2} & \color{blue}{7t} & \color{blue}{6} \\ \hline \color{blue}{2t} & & & \\ \hline \color{blue}{1} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{t^2} & \color{blue}{7t} & \color{blue}{6} \\ \hline \color{blue}{2t} & \color{orangered}{2t^3} & \color{orangered}{14t^2} & \color{orangered}{12t} \\ \hline \color{blue}{1} & \color{orangered}{t^2} & \color{orangered}{7t} & \color{orangered}{6} \\ \hline \end{darray} $$Combine like terms:
$$ 2t^3 + 14t^2 + t^2 + 12t + 7t + 6 = \\ 2t^3+15t^2+19t+6 $$This page was created using
Polynomial Operations Calculator