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